Here was the flight path:

https://makingmaps.files.wordpress.com/2011/10/makingmapsannotatedvoyagermaps.pdf

Here was the flight path:

https://makingmaps.files.wordpress.com/2011/10/makingmapsannotatedvoyagermaps.pdf

And you can draw this up on a Flat Earth map just as easily.

The link in the OP won’t open for me but its good Sean started the discussion.  I’ve wondered why someone, anyone, doesn’t just do a simple experiment and settle the question.  All that is required is the ability to navigate a flight path in a straight line.  It doesn’t matter where one starts, but I’ve selected a particular path because I’m familiar with it (I use to live in Colombia and I worked for a few months in East Africa).
 
1.      Start at Bogotá, Colombia’s Eldorado International Airport (latitude = 4.624335 north) heading due east, just north of the equator.

2.      Crossing the Atlantic Ocean and arriving at the west coast of the African Continent, stop at Leon M’Ba International Airport in Libreville, Gabon (latitude = 0.390100 north).  The plane can be refueled, provisions taken on, and everyone can get off to stretch their legs.

3.      Taking off and heading due east across the African Continent there are two good choices for a place to land, refuel the plane, take on provisions, and where everyone can get off to stretch their legs:
a.      Entebbe International Airport in Uganda (latitude = 00.020 north);
b.     Jomo Kenyatta International Airport in Nairobi, Kenya (latitude = 1.31916666667 south)

4.      Now the expedition heads out again, traveling due east and more or less along the equatorial line.  This route takes one out across the Indian Ocean to the island of Sumatra in Indonesia and then the Indonesia part of the Island of Borneo.  There are several airports one could land at.  For this example I selected Changi International Airport in the City State of Singapore (latitude = 1.359167 north).  After taking on fuel and provisions and our intrepid explorers having had the opportunity stretch their legs, it is now time for the final leg of the journey, regardless if the earth is a flat plane or a sphere.

5.      Taking off from Changi Airport the plane is again heading due east across the Pacific Ocean more or less following the equator.  On this route another land mass  or “solid feature” won’t be encountered until either:
a.      The plane arrives back at the West Coast of Colombia, having circuмnavigated the globe, or
b.     The plane arrives at the end of the flat earth plane, or the “firmament”, or whatever is out there “on the edge”.
 
As it may come up, and one of the posters on this thread loves to bring it up, let’s talk about the Antarctic Treaty:
A.     This treaty was signed on December 1, 1959, so it had ZERO impact on the thousands of explorers before then who have probing the earth’s boundaries for millenniums, and none have seemingly been to the edge.

B.     The Antarctic Treaty ONLY applies to the earth territory that is “beyond” or “past” or “south of” latitude = 60 degrees south.  As one will observe, the path of exploratory travel I described stayed with a range of 4.624335 north and 1.31916666667 south.  It went NOWHERE near the area covered by the Antarctic Treaty.
 
 

Yeah, Sean, that's a weak sauce flight path. You need to show one that goes pole to pole. I saw a docuмentary a few months ago of a pole to pole circuмnavigation, and it was garbage. They did it during the northern summer, and practically skipped showing them fly over Antarctica because it was pitch black outside. I think they even claimed to have debunked flat earth just by flying over the north pole if I remember correctly, long before they supposedly flew over the south pole.

I think they could put FE to bed very easily for a fraction of NASA's budget for one day.  There are planes now that could circuм-aviate the circuмference of Antarctica without refueling and return to somewhere like Argentina.  They could put a bunch of FE observers on the plane with whatever scientific equipment, and also use some of their own, then station some vessels around the perimeter of Antarctica to observe the plane, and have those on board confirm that the coastline (ice) always remains on the same side of the plane, depending on whether they were going clockwise or counterclockwise.  That's all it would take to end the debate once and for all.  Then they would have to come up with some explanation for why we can see too far.

Also, the videos out there purporting to show the 24-hour Antarctic sun (which would also cause issues for FE) were demonstrably fake ... where identical cloud patterns or sun rays, etc. were seen at the beginning and the end of the video that claimed to show 24-hour sun.  Another one clearly was spliced, where you can see shadows moving around these flags, but then they would suddenly skip and appear like 100 degrees further around the flag.  So why fake these videos when it would be a simple thing to film this unedited.  Of course, as we get more and more advanced with CGI, Photoshop, and other technology, the time is quickly drawing to an end where videos can be used as proof of anything.

Some have claimed to cross Antarctica by land, but if you look at the route they took, they were actually making a cross-section of a side of Antarctica.  It would be nearly impossible to make a direct line across it anyway, given the terrain.

I found this amusing:

Can you fly over Antarctica?

Yes, there are two ways that you can fly in a plane over Antarctica. Whether you're doing it to prove the flat-earth theory or just to have fun, you'll need to choose one of these options...

https://www.spacecentre.nz/resources/faq/solar-system/earth/flat/antarctica-fly.html

If the Earth is flat, and  cameras are used to try to prove it, why do photographs/images of the Earth from space fail to show every continent ?

Space is fake, that's why, and most NASA photographs are fake.