Dave, have you ever seen Bob Enyart's "The Planets, Stars, and the Bible" video? If ever there was a final nail in the coffin of this ridiculous conspiracy theory, this would be it (at least for those who believe the Bible).
In it, he talks about the constellations. He talks about the stars themselves. And he talks about how they represent the story of the Bible.
He then uses a program called "Dance of the Planets" (which is still available for purchase) to show what the star of Bethlehem was, an alignment of the star Regulus and the planet Jupiter, NOT ONCE BUT TWICE, both times being recorded in the Bible, the first time when Jesus was born, which the Magi followed, and then the second time some months after Jesus was born.
There is no model that the flat earth provides (that I'm aware of, and I'm willing to be proven wrong) that explains the movement of any of the celestial bodies. The movement IS explained, however, by the Heliocentric model of the Solar System. Jupiter lines up with Regulus (the root word of which is where we get our words "regal", meaning royal) the first time in 3 B.C., and again in 2 B.C., which is when the Magi would have arrived in Bethlehem.
The night sky itself is evidence against the earth being flat, Dave.
We'll see.
--Dave