Can a Flex App be a Websockets client?

I don't see why not!

Has somebody implemented this so far? Any links?

If n开发者_如何学Goot, I will! :-D

Yes. There is a Socket API that could be a Websockets client. Also check out Kaazing - a Websocket server with a Flex client library.

Yes. look at GraniteDS, if your backend is in Java. It has everything you need. There is also an example application showing chat using webscoket.