So according to the flat earth paradigm, would it mean that the sun does not literally rise and set, even though Scripture says it does? 

Or would it be argued that there is a sense in which "rise" and "set" could be interpreted in regard to the flat earth paradigm?

However, what's NOT the same is when you apply FE or GE to something like the book of Joshua.

Remember when Joshua prayed that the sun would stand still, and lengthen the day, so they could pursue their fleeing enemy?

In the GE model the earth would have to stop spinning, which would cause everyone to suddenly fly through the air at hundreds of miles an hour. Massive tsunamis would have occurred. It's ridiculous when you think about it.

Long story short, people who are taught MODERN SCIENCE are going to tend to dismiss the historical accuracy of that event. They will dismiss it as an allegory, fable, myth, or something similar. But they won't question the cosmological beliefs/opinions of mainstream science. They will sooner question the WORD OF GOD, HOLY SCRIPTURE than they would question or contradict the High Priests of "Science!" or "the Science".

So according to the flat earth paradigm, would it mean that the sun does not literally rise and set, even though Scripture says it does?

Or would it be argued that there is a sense in which "rise" and "set" could be interpreted in regard to the flat earth paradigm?

Sungenis admits that even with the geocentric or heliocentric models, the sun doesn't actually "rise" or "set", as it's rotating around the earth, but it's just a reference to the perception vis-a-vis the horizon.  So in terms of Sacred Scripture, Sungenis focuses on the fact that the earth doesn't move.

Nevertheless, that is simply the case with one FE model.  There are others which have the sun moving around a spherical firmament.  Another model, as proposed in the Book of Enoch, does have the sun moving up and down in the firmament.  BTW, Sungenis makes the same mistake attacking FE, as he attacks some aspects of the most common FE model as if the model were synonymous with FE.  It's not.  While there are certain problems with any FE model that could falsify FE, thus far the ones I've seen might (if true) invalidate the MODEL but not FE per se.

Cf. 1:45 - 3:00
https://ms-my.facebook.com/therealrobertsungenis/videos/live-conference-the-catholic-church-on-geocentrism-scripture-and-fathers-robert-/1255222044951669/

So ... fail.

That's pretty much as far as I got in this video, but it's interesting that you make this post literally about an hour or two after I saw this.  This is where I also saw the other links, including to his video about the "Errors of Archbishop Marcel Lefebvre" made about 2.5 weeks ago with Salza.