St. Augustine taught it around 1600 years ago and it is still true today:

It is also frequently asked what our belief must be about the form and shape of heaven according to Sacred Scripture. Many scholars engage in lengthy discussions on these matters, but the sacred writers with their deeper wisdom have omitted them.   Such subjects are of no profit for those who seek beatitude, and, what is worse, they take up very precious time that ought to be given to what is spiritually beneficial.

What concern is it of mine whether heaven is like a sphere and the earth is enclosed by it and suspended in the middle of the universe, or whether heaven like a disk above the earth covers it over on one side?...
Hence, I must say briefly that in the matter of the shape of heaven the sacred writers knew the truth, but that the Spirit of God, who spoke through them, did not wish to teach men these facts that would be of no avail for their salvation.

Note that he says "the sacred writers in their deeper wisdom have omitted them."  He is saying that Scripture does not teach the shape of the earth.  Discussing this is "of no profit" and a waste of time.  The Holy Spirit did not wish to teach it because it does not affect salvation.

You say that you believe flat earth because of the teaching of the Fathers?  This is the Father whose teaching you ought to pay attention to.

Unlike flat earth, this teaching has persisted throughout Catholic history.  This is why Catholics felt no constraints against determining the shape of the earth using science.  This is why St. Bede, St. Hildegard, St. Albert, and St. Thomas were free to teach that the earth is a globe.  This is why globe earth could be taught in Church-run universities.  

And part of this passage "the sacred writers knew the truth, but that the Spirit of God, who spoke through them, did not wish to teach men these facts that would be of no avail for their salvation," was quoted in a papal encyclical.  It is not simply the opinion of a Father, but magisterial teaching.

It is Church teaching that Scripture is silent on the shape of the earth and that this topic has no spiritual value.  All your claims to be finding flat earth in Scripture mean that you are interpreting Scripture contrary to the understanding of the Church.

He's talking about the shape of heaven,
Not the shape of the earth.

They presumed it was flat. And the question was whether went around the flat earth like a globe, or whether it was just over it.

Nice try Jayne.

We've already seen that the shape of the earth is considered many times by Saints, including St. Augustine.  Was he wrong for doing it?  Obviously, this quote does not stand for all time or all situations because many Saints discussed this with regard to Scripture.  And with few exceptions, the far greater majority believed Scripture teaches earth is flat.  Most importantly, for out day and time, simple conclusions are easy to come to: 1. Scripture describes a flat earth. 2. Pagans describe earth is a globe.  3. Believe Scripture. 
It is so simple, it doesn't contend with St. Augustine's quote.  Nor be at odds with St. Thomas.  I'm not even sure one could say St. Thomas "taught" otherwise since he merely restated what Aristotle thought.  Lesson learned: don't listen to, or repeat pagans even if they're smart.     
In our time, the most erudite PD clearly encourages STUDENTS to consider and bring forth what Scripture teaches, as long as the Fathers elaborated on it, and that Scripture's words be interpreted LITERALLY.
Obviously, the OP is trying to cover up what is known.  For fear of the truth?  How much loyalty to worldly things must be given up in order to avoid what is not Godly?   Too much apparently.  Some are unable to break away, even from beliefs clearly rooted in paganism.   

We've already seen that the shape of the earth is considered many times by Saints, including St. Augustine.  Was he wrong for doing it?  Obviously, this quote does not stand for all time or all situations because many Saints discussed this with regard to Scripture.  And with few exceptions, the far greater majority believed Scripture teaches earth is flat.

No, St. Augustine does not speculate on the shape of the earth.  He occasionally mentions it when it is relevant to a theological problem. He is saying that his contemporaries who were trying to find the shape of the earth in Scripture were wrong. Even those who we now know are Saints. He is clearly teaching that Scripture does not speak on this.

And this is not just his opinion.  It is incorporated into magisterial teaching in Providentissimus Deus:

...the sacred writers, or to speak more accurately, the Holy Ghost "Who spoke by them, did not intend to teach men these things (that is to say, the essential nature of the things of the visible universe), things in no way profitable unto salvation." Hence they did not seek to penetrate the secrets of nature, but rather described and dealt with things in more or less figurative language, or in terms which were commonly used at the time...

The encyclical, not only states it as a principle that stands for all time, but broadens the scope. This is not simply about the shape of heaven and earth, but concerns "the essential nature of the things of the visible universe" in general.  The encyclical does not give examples of what it means by this, but obviously it includes the original context of the quote, the shape of heaven and earth.

And Pope Leo XIII, in this encyclical, backs up St. Augustine in saying that some of these Fathers had wrong opinions on these matters.

The unshrinking defence of the Holy Scripture, however, does not require that we should equally uphold all the opinions which each of the Fathers or the more recent interpreters have put forth in explaining it; for it may be that, in commenting on passages where physical matters occur, they have sometimes expressed the ideas of their own times, and thus made statements which in these days have been abandoned as incorrect.

The Church teaches that Scripture is silent on the shape of the earth.  Therefore Fathers who interpreted Scripture as teaching a flat earth were incorrect.  Therefore, people of our time who interpret Scripture as teaching a flat earth are imposing their own interpretation contrary to the teaching of the Church.

Catholics are free to believe the earth is flat if this is how they understand the science, but it is wrong to claim that Scripture teaches something about a subject that the Church says Scripture is silent on.

No, St. Augustine does not speculate on the shape of the earth.  He occasionally mentions it when it is relevant to a theological problem. He is saying that his contemporaries who were trying to find the shape of the earth in Scripture were wrong. Even those who we now know are Saints. He is clearly teaching that Scripture does not speak on this.

And this is not just his opinion.  It is incorporated into magisterial teaching in Providentissimus Deus:

The encyclical, not only states it as a principle that stands for all time, but broadens the scope. This is not simply about the shape of heaven and earth, but concerns "the essential nature of the things of the visible universe" in general.  The encyclical does not give examples of what it means by this, but obviously it includes the original context of the quote, the shape of heaven and earth.

And Pope Leo XIII, in this encyclical, backs up St. Augustine in saying that some of these Fathers had wrong opinions on these matters.
The Church teaches that Scripture is silent on the shape of the earth.  Therefore Fathers who interpreted Scripture as teaching a flat earth were incorrect.  Therefore, people of our time who interpret Scripture as teaching a flat earth are imposing their own interpretation contrary to the teaching of the Church.

Catholics are free to believe the earth is flat if this is how they understand the science, but it is wrong to claim that Scripture teaches something about a subject that the Church says Scripture is silent on.

PD does not say some of the Fathers had wrong opinions on flat earth.  If so, where?
Scripture is not silent on the shape of the earth no matter who says it.  Period. 
The Fathers who interpreted Scripture teaches flat earth were not incorrect.  No where is there proof of such an outrageous claim that the Fathers were incorrect.
Any drawn conclusions from errors like this are proven incorrect. 

Saint Augustine said that Scripture was silent on the shape of the heaven and earth.  This was obviously accepted by Catholics throughout the middle ages because they determined the shape of the earth with science, rather than Scripture.  Then Pope Leo XIII said it in an encyclical.  When something has this much support from Tradition, we should accept it as true, even if it does not fit our pet theories.

A papal encyclical explicitly stated that the Fathers could have incorrect opinions on things like the shape of the earth.  Church teaching shows that the Fathers who saw support for flat earth were wrong in their way of interpreting Scripture.

This statement of Augustine wasn't accepted because many Saints DID talk about it.  Before and after St. Augustine.  And Scripture talked about it throughout the texts. Science must be in accord with Scripture or it's false science.  And spherical earth is not in accord with Scripture.  The Encyclical you speak of even says that those who hold to the LITERAL interpretation of Scripture can expound on the issues of science.  To suggest otherwise is proven false by Saints, Scripture and PD.   

Spherical earth is not in accord with a particular interpretation of Scripture (associated with the Antiochian school of exegesis) that was never adopted by the Church as a whole. You do not understand what PD is saying about literal interpretation.  

There has been over a thousand years in which the consensus and practice of the Church was based on the assumption that Scripture did not teach that the earth was flat.   This is why virtually all Catholics since 700 AD believed the earth is a sphere.

The flat earth movement of the last century or so was started by Protestants.  These are the people who might think that Scripture teaches flat earth. Catholics believe that Scripture is silent on the shape of the earth and this belief has existed since the Patristic period.

Spherical earth is not in accord with ANY interpretation of Scripture.  No one uses Scripture to teach earth is spherical.  Yet, many Saints and ancients both describe from experience and from Scripture that earth is flat.  
The flat earth "movement" wasn't started by Prots, but it was certainly maintained by many Prots.  Flat earth is ingrained in the hearts and minds of those who read Scripture and Catholics who appreciate the Saints and Scripture. 

St. Augustine taught that Scripture is silent on the shape of the earth and this view was, in time, accepted by the Church and eventually incorporated into magisterial teaching.

Of course, nobody uses Scripture to teach that earth is spherical.  Since Scripture is silent on the shape of the earth, nobody ought to use it to teach that.  Those who seek to learn the shape of the earth through science rather than Scripture are being good Catholics.

The Saints who interpreted Scripture as saying that the earth was flat, for the most part, did so before St. Augustine taught that Scripture was silent on the subject.  

Catholics who appreciate that Scripture must be understood with the mind of the Church do not look for the shape of the earth in Scripture.  Flat earth is the domain of those who, like Protestants, understand Scripture according to their personal interpretation.

St. Augustine is not the Church.  He disobeyed his own statement, so he either didn't mean it as you think, or it wasn't important to him.  But that doesn't mean it isn't important.
There were other Saints and Catholics who spoke about the shape of the earth after St. Augustine. 
It is impossible to miss the shape of the earth in Scripture as the Saints themselves explain.  Just because one guy didn't think was important, spoke about it anyway and others spoke about it, shows that your premise is devoid of value.  Making stuff up against the evidence available is very untoward. 

He has passed over in silence, as useless, all that is unimportant for us.

.
Good thing then we're focusing on what's really important for us.
.
Didn't you say you were going to give flat-earthism a break, Jaynek?  What happened?  
.
Matthew's detox suggestion didn't work, eh?   ;D