Recently I went to a talk about the Flat Earth phenomenon and what's causing such an easily disproven myth to gain traction. It was pretty interesting. I'll just share a few highlight points in case anyone here ends up talking with one of these kind of people.
1) Often they are not flat earthers because of a complete lack of scientific knowledge, but because of being misled by poorly executed science and experiments. Often on Youtube - people doing flawed experiments or reaching the wrong conclusion from the experiments they have done (such as seeing if a spirit level remains flat while on a plane and similar).
2) Flat earthers often - very often - link in with many other conspiracy theories. This can range from "the Moon landing is fake" - which makes sense if you think space is fake - right up to much more sinister things such as Holocaust denial and similar. Be careful.
3) Perhaps most important (which is why I buried it as number 3, go me) there isn't just a single "flat earth" model that's agreed on. Talk to 10 different flat earthers* and you'll get 10 different ideas on what the Flat Earth is, how it works and why it works. In fact there are schisms in the community, with some sides basically claiming the other are government shills designed to mislead people and discredit the theory. Yup, it's an, uh, interesting community.
4) When interacting with this kind of people, it is very easy and tempting to act smug and conceited since you know you're right and they're wrong. And of course, you are - but bear in mind from their point of view, they're right and have realised something you've not, and so this attitude often only further serves to reinforce. Don't take an aggressive or superior approach.
5) Similar to the above, but how often do you interact with Flat Earthers and hear their arguments? Probably never, right. They interact with us every day, and hear the same arguments constantly. They have answers to them. If you come out all guns blazing and argue points, they will usually have an answer to you because they already thought of it, and unless you are a serious expert at physics (usually) there's a high chance you'll get caught out in being unable to answer them eventually - you're dropping down to their level and they beat you through experience. Instead you're generally better off talking with them and getting them to try and explain their views. You don't have to lie and pretend to agree, just try and follow their line of thought, as though it might hold some merit - and ask them to clarify and explain points that you feel are incompatible with what you've seen/know from reality, rather than directly challenging them. This won't get you an instant "win" but that's because you stop it feeling like you vs. them. Instead you can act almost like a guide to them, making them question it for themselves. Remember what I said - a lot of these people aren't completely ignorant of science, they've just been deceived by bad science. If you can guide them into doing things right, there's a good chance they'll work out their mistakes.