True, according to the documentary, the south pole is the edge.
Therefore, all you'd have to do is fly across the south pole to debunk flat-earth.

However, what would happen then?
No one is going to change their mind.
The evidence will simply be bent around the assumption:

You faked the video, or it's pac-man rules where you go in on one side and come out the other, or your voyage was simply an illusion, or the edge is defined in some other way.

This is why I make the claim that this is a faith-based argument,
because everyone is begging the question and assuming the conclusion is true.

This is why we need to stop trying to provide evidence and animosity in the face of faith-based arguments, and instead attempt to provide trust and love. No one changes their mind because they were insulted or ridiculed; quite the opposite really.