While working on the cosmos of a flat world, I came upon the idea of using a dim sum rotating about an axis through the central pole (as described here) in order to accomplish days and seasons. The sun would rotate around the pole of the world with a 1 year period, and a moon would rotate closer to the plane of the world with a larger orbital radius and an orbital period of one day. In this way, night is formed by the umbra of the moon passing over the world as it eclipses the sun, and seasons are formed by the physical distance from the sun to the plane of the earth. However, when trying to work out the orbital periods I realized that the angle from a point to the sun varies over the course of the year, which might impact the required course for the moon to keep up the daily eclipse. Under what conditions would this world receive earth-like brightness during the day over the course of the year (and seasonal temperature variations) but still get 12-hour lunar eclipses for nights, every 12 hours? Is it only possible for a particular sector of the world to receive earth-like cycles, and other parts of the world will simply be exposed to some extreme conditions? Adverse effects of gravity due to the proximity of the bodies can be handwaved away, as this is a flat world.
I don't mean to be obvious but there are flat earth theorists who have theories on this in the real world.
The way I understand it is that basically the sun is a spotlight and points at different parts of the earth at different times, the moon and stars are points on a black background that move in odd ways and I am not sure how they explain seasons.
I would suggest that you research that stuff to get some kind of scientific logic in a flat world scenario.
I just want to point out that I do not believe in this crap, I have an uncle who does and will not shut up about it. The reason I mention it is that they have, at least, semi-plausible explanations for inconsistencies.
The biggest problem I see for a flat planet is the gravity of the planet itself, there is a vsauce video on youtube which explains this here: