I'm sorry but to me the association of Flat Earth and General Relativity seems almost laughable.
With the all of the matter in the universe is contained in something like a hemisphere of what size?
Who knows? There seems to be no real agreement. Some say there's an impenetrable dome up there, so I'll guess at something like 40,000 km diameter and 20,000 km high (I'm sure some knowledgeable FEer will correct me).
Anything travelling fast enough to see any relativistic effects (outside particle accelerators[nb]and many seem to think they are fake anyway![/nb] would collide with the "dome"). We can't have satellites in orbit, and even there relativistic effects are minimal.
We are told that GPS doesn't use satellites, so it doesn't need relativistic velocity or gravitational corrections.
From what I can see on a flat earth, who cares about General Relativity?
It might come into UA, but in my opinion UA itself is really on shaky ground.