First, keep in mind that just flagging a single comment as "too chatty" is more likely to, if we think the flag has merit, see that one comment deleted; when we view comment flags in the moderator dashboard, we see them out of context. Specifically, we only see flagged comments, not the discussions surrounding them.
The software will automatically suggest moving comments to chat if it detects what appears to be significant back-and-forth. I don't know the exact heuristics used, though; they are probably described over on Meta Stack Exchange somewhere.
If it does that, you can just opt to migrate the discussion to chat. Note that the comments aren't actually moved, just copied. You can then flag the post and request a comments purge.
An alternative is to flag, ideally (in my mind, at least) the post the comments are attached to with a custom reason, and request that comments are migrated to chat and purged. If you do so, one flag is perfectly sufficient and it's easy for us to see what's needed. A moderator can transfer the comments to chat at any time, including migrating further comments into an existing chat room if needed. (The latter is not always ideal, but the option is there. Better to try to actually make people continue the discussion in the chat room if possible.) This ability is however no excuse for keeping up a conversation in comments and expecting us moderators to clean up after you. If we have to do this repeatedly, particularly on the same post (yes, we have Ways(tm) to tell), be aware that it is actually easier for us to just lock the post permanently for off-topic comments and nuke the comments from orbit. That is probably not what you want us to do...