Now that's an interesting question because, if the earth is flat, it presents some problems.
The usual FE notion is that flat surface of the earth is atop something substantial, like a huge tree stump, or a pillar, or a stack of turtles. Which means that, though the sun (and moon) may go straight east to west, once they are over the horizon they must take a detour around the stack of turtles to get back to the proper rising position in the east.
A minority FE notion is that the flat surface actually spreads out to infinity, which means there is an unlimited amount of territory (and/or ocean and/or ice) beyond the known geography in all directions -- a very tempting opportunity for exploration and exploitation -- but that raises questions of where the sun (and moon and stars) go when they go down in the west; apparently they cannot go down below the horizon, they cannot go under the surface of the flat earth from the west to the east, so apparently the sun, moon, and stars catch a train in the west that chugs around the known earth in exactly 12 hours to enable them all to rise in the east at the appropriate time.