I know what the solar system model is for heliocentric and geocentric. I cannot visualize what the solar system model is for a flat earth.
The simplest way to understand FE is that the solar system still exists, but it's much, much closer to us, because it's within the firmament. Instead of a star being "millions of light years away", it's probably only 500-1000 miles away. Far enough that the naked eye cannot see them in daylight; but close enough that their lights can be seen at night. The sun is not bigger than earth; but much, much smaller and inside our atmosphere. The sun moves above the earth, from east to west, on a daily basis. Because it's smaller, it does not give light in all directions, but is more focused, like a spotlight. Thus when it's spotlight turns, and as it physically moves away from us, it has the appearance of "setting".