As explained on QI, and many other places, almost no-one in human history ever actually thought that the world was flat anyway. The Ancient Greeks knew it wasn't, as did the Babylonians, Romans and mediaeval explorers. When standing on a tall cliff looking out to sea, the curvature of the earth is perfectly visible. The ancients watching their ships disappear over the horizon didn't think they'd fallen off the edge of the earth - especially when those ships returned to port...
I've just had a look at the flat earth website. My favourite part is their "explanation" of gravity. Apparently gravity is caused by the Earth constantly accelerating upwards at 1g!
Now seeing as a constant 1g acceleration would mean getting to light speed in a a little under 1year (354days) that would mean the earth is currently moving at something like 4 billion times the speed of light.
When I was at school a member of the FES gave us a talk. Part of his argument was that as no one understood relativity it couldn't be true! I believe that the FES originall existed simply to contradict scientific dogma (to prevent it becoming like religion). It seems that some members aren't aware of that.