I think Flat Earth is to conspiracy theories as Flying Spaghetti Monster is to religion. Nobody actually believes in the Flying Spaghetti Monster. They just pretend to believe just to mock those people who believe in a guy who walked on water and came back from the dead.
If these people are making you mad, ignore them. Don't give them the attention that they crave.
I suppose some Flat Earthers actually believe that the Earth is shaped like a pancake. I don't know what you can do for these people other than invite them up to the top floor of a skyscraper or take them on an airplane ride. People got along fine for thousands of years believing that the Earth is flat. As long as these nitwits don't try to fly planes, sail ships, or attempt any activity that requires that they know the Earth is round, flat Earther will get along fine believing whatever they want to believe.