Why can't you write one yourself using for example one of the freeware server side solutions, like Red5 or Blaze Data Services. Writing a chatroom in Flex, basing on those technologies should be less than 50 lines of code - believe me, I've done that many times.
True, it's not something so hard that you can't do it yourself. "Flex Message Service" is a good topic to learn.
One example (there are others):
Now, if you want something very fancy with lots of bells and whistles, that would be a little more work. I'm not aware of any "fancy" solutions out there.
In adobe website there are a lot of showcases that you can base to do this. In special you can see and get source code of this sample http://www.adobe.com/devnet/flex/articles/help_callcenter.html that use BlazeDS to send and receive messages.
Just Google "free flash chat room"