Flat Earthers and what to do with them

Coming from a background in physics I find it really hard to understand people's logic when I read these theories

It's not logic, it's emotion. If there were logic, honest investigation would lead to discovery of the truth. This is why most people who call themselves "skeptics" are not - they're not skeptical of everything, just anything "official".

Most conspiracy theorists are buying into it because it instantly makes them feel more intelligent than everybody else, particularly those with more "officially sanctioned" education/training than they have. It's very close to the reasoning that tempts people into religious cults (for which reason, I have little sympathy for cult members - they want to be told that the rest of the world is evil and they're in the tiny virtuous minority).