I'm amazed that no one has come up with the simplest explanation (Note: just using the conspiracy BS to fit in with FE fantasy, not claiming reality):
The flight times are not indicative of distances.
The planes/boats/etc are capable of travelling much faster than people think and they travel much faster south of the equator to keep up the conspiracy that the earth is a globe.
I would suggest this as a more accurate map for a flat Earth (not exactly flat, but more like a bowl) to explain the flight paths. A completely flat Earth wouldn't be able to explain the motion of the sun in a straight arc at the equator at September 21. Also, in the image provided, we should realize that the curvature would be a lot more pronounced than that. Only differences between this theory and the one that the Earth is a sphere is that it is more flattened at the north pole and the Earth curves back away from the north pole after reaching the equator. The flight paths wouldn't be much longer at the tropic of Capricorn than they are at the equator. However, it would still be shorter to go through the northern hemisphere to reach the other side of the Earth.
Not that I am completely convinced that the Earth has that shape, but it works with the actual known astronomy except for the region near the south pole (which no independent researcher can visit as of now).
And I would discard it as nonsense.
It cannot explain any of it.
It doesn't explain why at the equinox the sun appears to rise due east and set due west, following a straight line for the people on the equator. For the people on the equator, that model is pretty much the same as a flat Earth.
That model just helps with distances in the northern hemisphere and helps explain why the north pole can receive some darkness.
It doesn't help much for the southern hemisphere. Especially not for those flights. With that model, the further south you are the longer the distance, so it makes no sense for the flights to go south.
And independent researches can go to the south pole. It is just quite expensive and dangerous.