Laugh all you want, hell, I'm laughing, but the OP is right, The Flat Earth Society really does exist. It's been around for decades. Thomas Dolby ("She Blinded Me With Science") is a charter member! His second album was titled "The Flat Earth".
Not saying I believe them, just saying that they do, indeed, exist.
Also, there are people who believe that "We never went to the moon"!
I'm sure that somewhere out there, there's a group of people that believe that the Earth is held in position by resting on the back of a giant turtle!