My wife and I deal with something similar. Her brother is part of the Hebrew Israelite movement, that absolutely loves to debate. And while I'm fine with debating and proving facts through scripture, they don't debate, they like to control the conversation and have it one way.
We've come to the conclusion that....All you can do is pray lol As simple as a solution as that sounds, I just remember scripture when it comes to dealing with division, debates and the spirit of confrontation.
Might not be the answer you are looking for when it comes to the flat earthers (they are fun) but that's all I know how to deal with things like this....Make your point, provide truth and if they don't want to hear it, all you can do is pray.
Debate is healthy only if both sides are willing to change their minds should facts challenge their thinking. I've found that most people aren't willing to change the way they think about things even if facts can show that they are wrong. We live in an age when people are more than comfortable changing the facts at their discretion or choosing which facts they wish to believe. It can drive a thinking person insane, if you let it.