Come on, of course the world is flat! Didn't you read Terry Pratchett? The Discworld is carried through space on the back of the giant turtle A'Tuin!
Joking aside, considering the huge number of official lies we're fed, I don't think it's surprising people begin to doubt even the most obvious things...
And since you've spent time talking to flat-earther did you find out why this huge conspiracy? What's the point of hiding the fact that the earth is flat???