To a flat earther it cannot be proven. The flat earth society started out as a philosophical movement stating that one should only believe what can be directly observed. Since then it has evolved into something much more mundane, little more than a run-of-the-mill conspiracy theory. Come to think of it, the flat earth society itself must be at least partially responsible for the rise of BS:
Edit: A flat earther could of course get a ride in a fighter jet if he wanted to challenge his notions, but that is beyond the means of most. Still, there are those who try.