The wiki article provides a thorough explanation for the perceived weaknesses in astronomy - perturbations, three-body problem etc. - it is an interesting read, but does not explain how solar eclipses work on a flat earth. The solar eclipse page explains how eclipse paths look nicer on a flat earth map, agrees that the cause is the moon blocking the sun, but no other details are provided.
Are the sun and moon the same size, roughly the same height above the disk? Does it get colder during an eclipse because the cold lazer light emitted from the moon is blocking all the hot sunlight? Do the lengths of the shadow paths make sense with the orbital velocities of the two bodies above the earth's plane?
I'm not pretending to have any answers, this stuff is out of my wheelhouse, but I'm very curious how it works.