The flat Earth concept can be destroyed on any clear night by observing satellites in the sky, provided one accepts either common sense or sanity as valid stances.
Unless governments around the world are launching one-shot satellites every night to maintain the conspiracy, or using holograms to project satellites into the night sky (or something equally insane), a flat Earth simply won't support a constellation of orbiting objects. They'll fall right over the edge, giving you nothing but blurry images.
Worth noting is that spherical trigonometry and astro-trigonometry are exact sciences, which only work in a spherical environment.