Whether or not something qualifies as a flame is so subjective. Personally, I think we should keep things as-is because flames speak for themselves and no one is forcing anyone to read.

If people want to engage in written abuse of others (read: make themselves look stupid), so be it.

One other, maybe too-involved option: on each and every post (only signed-in users would see this) have a simple image button that would mark the post as a flame.

So, if I personally think something is a flame, I can mark it.

Now, the aggregate votes of the other users would at some point (e.g. 20 votes) cause that post to be hidden from view (as well as all replies to it and/or quotes of it?!?!). I still don't think it should be deleted, but maybe you use a collapsable <div> tag in place of that post (or posts) so that those that don't want to read it can simply bypass it (although everyone loves to read a good flame war now and again!).

I must be really bored to be putting this much thought into it!