A lot of the flat earther stuff stems from a description of the planet from the old testament. Many flat earthers believe there is a clear dome over the earth.
http://www.philipstallings.com/2015/06/the-biblical-flat-earth-teaching-from.html?m=1
Most of them don't believe in gravity because gravity couldn't work the way we observe it if the earth was flat. They have a theory of density instead. Most of the flat earthers believe the sun is only a couple miles across and it works like a spotlight. Most of them believe the moon creates its own light and moonlight has a cooling effect opposite of the sun's warmth. They believe Antarctica borders the entire earth and that there is a global conspiracy to keep people away from the edge and that anyone who tries to see the edge is captured or killed.