As it has been said, there is no consensus about the shape of the earth, aside from its flatness. Some claim it's like the map you've posted, others think it's a concave half torus, others think the map is actually a sphere because the flat earth's measurements are warped by some extrapowerful force making it non-euclidian, etc.
So there can't be an acceptable answer, other than "those flights are fake/You're not actually going where they tell you you're going/weird science fiction technology lets planes travel faster as they get closer to the south pole (which according to most flat earthers, doesn't exist because the Antarctica, being a ring, doesn't have a single point furtherst to the north pole)".
As it has been impossible to create a flat earth map, it would not be farfetched to think there could be other continents or even other flat earths with their own domes, suns and moons. But only if the flat earth rests in an infinite space.
No flat earth model can explain moon eclipses (nor solar ones, mind you). To give an answer, it's either bioluminiscent lunar creatures or an invisible third object flying over us that, even if it is invisible and transparent, can still cast shadows and light, alternatively, at the best convenience of flat earthers.