Your comment immediately reminded me of yet another "relevant xkcd": http://xkcd.com/1235/
Regarding some of the other comments here, my sense is that there are some beliefs where mockery really is the best response. (Hopefully not mean-spirited mockery, mind you.) If you engage with flat-earthers on a serious level, you inevitably wind up lending them at least a bit of an air of legitimacy (in the eyes of outsiders who may not yet be familiar with the topic in detail). If you ignore them, they can monopolize the public discussion and claim that you're afraid to face their ideas. Laughing at their ideas can be more effective in both ways, at least if handled well.
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Your comment immediately reminded me of yet another "relevant xkcd": http://xkcd.com/1235/
Regarding some of the other comments here, my sense is that there are some beliefs where mockery really is the best response. (Hopefully not mean-spirited mockery, mind you.) If you engage with flat-earthers on a serious level, you inevitably wind up lending them at least a bit of an air of legitimacy (in the eyes of outsiders who may not yet be familiar with the topic in detail). If you ignore them, they can monopolize the public discussion and claim that you're afraid to face their ideas. Laughing at their ideas can be more effective in both ways, at least if handled well.