After reading Bishop's response, I'm left with more questions than answers. It's unclear how two celestial poles would ever be seen from the surface of Flat Earth. Personally I would love a more clear/explicit explanation of the forces governing apparent stellar movement in the Flat Earth model, because this is something about Flat Earth theory that has never been entirely clear to me.
A more simplistic way to put the question might be "Why is Polaris not visible in the southern hemi-"sphere?" This is a well-documented phenomenon which seems impossible on Flat Earth; no matter where you are, you ought to have line-of-sight to Polaris. I assume the Flat Earth explanation involves light "bending" in some way, but 1) that seems pretty well dismissed by this thread:
https://forum.tfes.org/index.php?topic=6692.msg122178#msg122178 , and 2) I have as of yet seen no well-formulated mechanism from the FE community which would explain why the light bends, how much it bends, etc in such a way that it can be reconciled with what is observed. On the Globe Earth, there is such a comprehensive theory, which involves the earth being spherical, stars being relatively stationary and distant, and not much else. Because at this point in time GE theory is vastly more useful in explaining the motions of stars, it is obviously the superior scientific model with respect to stellar movement (not to say anything of "truth").
Anyone from the FE community want to offer up a comparable explanation for stellar motion? I understand the FE camp does not have a "unified" theory in the same way the GE camp does, so it's totally possible a good explanation exists that I haven't come across yet.