first of all, disclaimer: i do not believe the earth is flat and in this topic i would like to provide a simple reason why.
My main problem with your theory is the fact that time zones exist. Unlike "ships going past the horison" there is no possibility of light-bending cold air, no optical illusion that can be utilized to disprove the existence of time zones, and, on the contrary, proving their existence is nowadays easy, any videochat (skype or viber), any webcam can prove that the day/night cycle is different in other places on our planet.
If you would consider the traditional astronomical model the explanation is easy: light from a distant sun illuminates only half of the Earth sphere, and the other half is dark. As the planet turns, some places get under the sunlight while other turn the other way around, hiding from the sun. I don't know any coherent explanation that would make time zones compatible with flat earth.
Let's consider two models describing sun in the flat earth model:
- Sun goes around the disc
In this model sun makes a full revolution around a disc, going below the plain at night. This model makes pretty nice sunsets and sunrises, but then the how could there possibly be any time zones? More still, if you would assume that this flat earth is radial and centered on the north pole, the sun would rise from different directions in different places. - Sun goes in circles over the disc
From what i saw it seems that the second model is more popular, having even some explainations for seasons. However, this model makes no sense out of sunrises, and day/night cycle seems just as improbable.
Do you have any models that actually work? i can make some 3d models to illustrate them.