Sorry, but this unregistered user can't think up any good ideas, you all couldn't have asked first before you closed it so some of us who think beyond the "norm" could come up with something for you. (notice I say ALL, meaning all the mods here)
It's simple, you have a link between normal posts that says something like "read unapproved post from anonymous" or "approve post from [first name]" and people can click or not click. When they click two buttons come up at the bottom that says "vote, is this flamebait?" and if enough DIFFERENT people say no then it's posted as a normal post with the ID anonymous. If enough say yes, it's removed completely.
Think about the free time you mods will have then!
If it needs to be edited then that's another story, but you could have another button for that "needs editing" and it's sent elsewhere if enough people agree.
Yes, it's a problem because it's not part of this typical software, and I just gave away the hot new killer feature for forums like this and now someone else will make $$ from my idea as usual.
So if you ask nicely maybe some smarty here would be willing to write the php code to do that instead of cutting us crazy out of our minds non conformists off.