This is a topic of discussion, but it barely holds any merit or importance... honestly I like thinking about these kinds of questions, but I'm starting to think we could do with a science board alongside technology to discuss things like this.
But that's something for the Suggestions board, and I have a feeling there'd be little demand for it. In the case that this isn't a junk thread, I do have a response :V
...
Anyway, if we assume that we can ignore certain physical laws like gravity, and just add to the hypothetical that physics simply reworks itself in a way that this is plausible, then we can actually think about it.
The flat earth theory coincided with a geocentric model of the solar system (as purported by the actual
Flat Earth Society's FAQ, because they literally believe in this idea to this day), so we don't have to worry about things like the earth's rotation being changed. Everything would be more or less the same on a physical level...
Unfortunately, trying to read the rest of their site gave me brain cancer as they tried to explain things such as intercontinental travel and what lay on the edges of the world. So that's up to our own speculation for this scenario, unless someone else would like to sift through their logic.