What would convince me of a flat earth: as someone mentioned, going to the edge would very likely do it. Flying up and seeing it from high enough would probably work. Flying up and being able to verify the dome, and/or the "spotlight" sun and moon would be excellent. This would probably be enough to make me a believer.
Next best would be for other people to do the above, and do so in a repeatable, falsifiable way, whereafter other people are able to do the same, and others after that. This happening enough times would be a strong beginning, although I
suppose I could simply say all of these people are part of a conspiracy and being paid/coerced into corroborating the new flat earth paradigm. But who wants to be that cynical?

Barring that, it gets difficult. Photo/video evidence of the above would be interesting. Of course, I have to admit I would be the first to dismiss it as fake. So let's say if the photo/video evidence is analyzed by plenty of knowledgeable, legitimate experts in photo/video manipulation and declared legit, that's a start.
Some kind of smoking-gun evidence of the conspiracy. It would have to be out there. Documentation, recordings, etc. Again, these would have to stand up to scrutiny--any such thing could also be faked and there would need to be some reasonable degree of investigation, which ideally would uncover more such evidence that agrees with it.
Internal consistency within flat earth community--it would be marginally more plausible if they were all at least remotely on the same page.
Convincing alternative explanations for phenomena that are readily explained in the round earth worldview.
All of this combined would be enough, not to convince me, but to possibly make me a tentative round-earth skeptic. It would be enough to get me to think flat earth may be worth considering. But as far as "convinced"? I would probably have to see it myself.