First, let me say this site is fantastic. Who doesn't like a little nutty conspiracy theory once in awhile. I have a feeling that 90% of the supposed FE supporters are actually just faking it for fun or to encourage critical thinking. I do worry about the other 10% who are suffering from delusional paranoia.
I read the Wiki and there are some very glaring facts that blow this "theory" out of the water.
The sun and planets. So FET says the Sun is roughly 3000 miles away and is only 32 miles across. A few things. 32 miles is not large enough to create enough gravitational pressure to initiate fusion in hydrogen gas. (and we do know what the sun is burning because of its spectral lines) You lack the mass.
The planets are small and orbit the sun a couple thousand miles away. If this is true, why has no group of intrepid FETers launched a mission to these tiny planets to prove to the world that the Earth is flat? I think we all know that answer to that one.
Your model of sunlight is verifiable incorrect. If the Earth is laid out as proposed, some locations in the east would still be in daylight, while areas southwest would be in the dark. A simple phone call between two people, one positioned southwest of another could prove that the Earth is illuminated by this "flashlight" sun. Why hasn't this very easy, inexpensive test been done??? Again, we know the answer.
Edge continent that keeps the air in. LOL, hard not to laugh when typing that. Where is this 50K foot tall wall of rock or ice surrounding this flat expanse of land?? Surely it could be mapped by a simple mission. Again, the answer to why no one has done this is very clear. Also, the theory about dark energy holding in the air is completely false. Dark energy and matter are named that because they DON'T INTERACT with normal matter. It wouldn't be dark energy if it was holding all the air in. lol
There are many other obvious problems with FET - what causes this acceleration that gives the illusion of gravity, why don't the sun, moon, and planets simply crash into the Earth? I could go on - magnetism without a metallic core, the seaborne radar problem, the fake vanishing point argument. Good fun, but the believers in this stuff are...well, I'll be nice and say nothing.