All starting numbers for this calculation will be pulled directly from the FES wiki. If there is an issue with any of them, take it up with the editor of the wiki.
On the equinox, the sun is directly 90° above a point on the equator. At 45° latitude N and at 45° latitude S along the same line of longitude, the sun is seen as being at 45° up from the horizontal. The distance between the equator and these two points is about 3000 miles. Thus, the sun is 3000 miles in the air. Right? Well, let's see what happens when we shift around some, shall we? The sun should show up at that distance no matter where we look from, right?
Let's cut our distance in half, going from 3000 miles away and a 45° angle, to 1500 miles away, and a 67.5° angle. This gives us a sun height of... 3621 miles. Oh. Well that's quite a bit different isn't it? Well how about if we go the other direction. Halfway from 45° to 0°, giving us an angle of 22.5° and a distance of 4500 miles. This gives us a sun height of.... 1864 miles. Oh dear, that's even more out of whack than our first one. Well what about if we just go out to the poles. That's about 6000 miles, but to make sure the angle is above 0 like it is there, we'll go to just 5900 miles and see what the angle is there. This should give us an angle well under 10° at most. So with a 3000 mile high sun we get an angle of... 27°
Welp, I see three options here. 1) There's something making the light from the sun bend to get the correct angles all across the globe. It's consistent in all types of weather, all across the Earth, every day of the year. The only thing I can think of for this, is magic. Nothing else makes sense. 2) The Earth isn't flat. You can't have a sun that is simultaneously 3621 miles up AND 1864 miles up AND 3000 miles up. That's not possible. Therefore the idea of Earth being flat with a close sun, cannot work. 3) We have incorrect measurements somewhere. I started with numbers in the wiki though, and every other number simply follows what holds to be true mathematically. So either the wiki is wrong, or we're back to one of the other two options. Actually even if the wiki is wrong, that would leave us at one of the other options being true still.
So FEers. What's it gonna be? You can't have light traveling in a straight line AND a flat Earth.