Most FE models allow for the Stars to be what ever you want, so long as they are governed by different physics than the Earth. The general response is "so what?" The exact nature of the stars depends on which point of the Flat Earth you're trying to defend.
For example, if you're inquiring about gravity, then you may find the stars to be spheres.
If you're inquiring about the solar cycle, then you may find the stars to be travelling at near the speed of light, shining down a spotlight on Earth.
The simple answer is, they have no clue.
I find it ammusing, as my final project in a class as an undergrad was to make an accurate model of a red giant using python. Now, there must be thouasands upon thosands of these models created every year by students like me. Not a single model from the FE people. I've had a thread open for about a week begging for such a model from the FE community.