The sky would look the same---because the sky doesn't care what we look like. But we would only be seeing half of the sky, since a flat Earth cannot see the sky beneath it. As it is, we see the whole sky, only possible with a spherical Earth.

You pooh-pooh the rotation of the Earth because you are evidently incapable of computing the acceleration it produces, to find its magnitude and compare it to normal gravity. Thus, you defend your ignorance by hiding in ignorance.