I don't understand why flat earthers choose not to do this. It would be the easiest proof we aren't on a globe. All they have to do is follow some regulations and they can prove to everyone the "TRUTH"!
Which part(s) would be the easiest? Circumnavigate it by sea? Many have done it. There are even some sailing drones doing it now (Why, I do not know,
https://www.saildrone.com/antarctica). But you have to get there, get yourself passage on some vessel going the way you want to go. You could do what a couple of guys did a couple of months ago and race across it. Maybe get a job at your country's station there and steal a sno-cat and drive around the interior. Many more options I'm sure, but all of which seem at a minimum cost/time prohibitive.
And rest assured, even if some prominent FEr's did such a thing and come back and say, "Yep, there is no Antarctic ice wall," one or more of a few things would happen in the FE community:
A) Perhaps lean more toward a bi-polar model than the more popular FE AE ice wall model
B) Akin to A, the ice wall isn't Antarctica, it's further
C) Those claiming to have gone there are shills and lying and part of the conspiracy
D) Doesn't matter unless I see it for myself
Pretty simple really.