There would be no night and day. The reason we have night is because the world is rotating, and the sun light is blocked by the opposite side of the sphere. If the flat earth rotated, it would be day time all the time.

Assuming that the earth was stationary and the sun rotated around the earth would not cause us to need time zones either, because due to the great distance between the earth and the sun no matter where the sun was the light would hit us at practically the same angle, and we'd live under one time.