Well no nothing flies over Antarctic that I know of
And I'm not sure what theory it is that you think you're talking about...
My arguments for flat earth theory are arguments against ideas and motions that you believe occur on a spherical earth but that make 0 sense scientifically
For example with planes:
Since the earth supposedly rotates west to east at ~1000mph then all eastward directed flights should take longer than westward directing flights, since when flying east your destination should always be rotating away from you.
Not only that, eastward directed flights should have to fly an extra 1000mph ON TOP of their cruising speed to offset the earth's rotation in that direction
These are simple fundamental concepts of motion that even children can understand, yet it seems like people who are so absolutely positive that the earth is a sphere don't even attempt to think about, much less address
And there's plenty more naturally occurring phenomena that don't make sense in a spherical earth