To be a true flat-Earther (as opposed to pretending, as a game) you simply have to reject all reason. We understand the world around us by applying reason to observation. If you reject reason, then the observations are irrelevant. So what if the moon has phases? They are there to confuse scientists. So what if the sun or the airplane or the ship's sail, that's just to confuse you. Just as the creationist thinks that God or Satan put fossils in the ground to confound people who refuse to have blind faith.
I still think that most flat-Earthers are just pretending, because they enjoy making you hit your head against the wall, or they think that inventing silly excuses is a fun game.
My reply to flat-Earthers is to say that, no, the Earth is not flat, it's a sphere, but we are on the inside. Similarly, if someone says space aliens built the pyramids, I reply that, no, it wasn't space aliens, it was the Loch Ness monster who built them, by telekinesis, without ever leaving her Loch. And my reply to young-Earthers is to say, no, the Earth is not 6,000 years old: The FSM created the world seven days ago, including you and all of us with false memories of having lived our lives up to that time.
The only answer to bullshit is better bullshit.
Of course, you still need to educate people so they don't fall into those traps in the first place.