They mean “flat” in the sense of “straight” (i.e. not curved), the same way a sheet of sandpaper is flat despite being rugged. There are plenty of simple ways to disprove Flat Earth theories, but you’ll never be able to convince anyone by refuting their arguments with something which clearly misunderstands what they’re trying to say.

Take the piece of sandpaper and put a twist into it and now fold it back upon itself. Now it's not flat…nor is it round. It's a secret third thing.

Anyway fun topology aside a lot of flat earth discussion is not really done with the attempt to disprove anything, unfortunately.

Instead of refuting their arguments, ask them to prove it to you. Whenever they say something you don't understand, ask them to explain it. Eventually they will get stuck.