I too am having exactly the same issue (with a very similar project). Chrome will connect to a chat, but if you create one in Chrome and try to connect to it. It won't work at all. If you disable pepper (chromes sandbox flash plugin) and use the adobe version it works fine. Firefox/IE also work fine.
I've been trying to find a solution for a couple of days now and found nothing.
I'm hoping someone will be able to shed some light on this.
Thank you for your confirmation,
After some tests, I haven't been able to connect both browsers and I think there is no easy way to solve it by now.
On the other hand, I found a very interesting article (http://www.adobe.com/devnet/adobe-media-server/articles/real-time-collaboration.html) that solves in a certain way the problem using a fallback connection using RTMP with an FMS.
I know its not the ideal solution since it should be working with RTMFP but after reading the article I have realized that I have to implement the fallback solution for the people who have firewall configurations that restrict UDP traffic since it is going to be a public internet application
we covered this same cause in a different thread:
the issue is Flash Player in Chrome (pepper flavor) apparently doesn't send your local (behind-NAT) addresses to the server. you are behind a symmetric NAT (a different NAT translation for every peer you try to talk to), and/or you are behind a NAT that doesn't do hair-pinning (able to connect to another peer behind the same NAT via the NAT's external address). you can use
to diagnose what kind of NAT you have.
most likely the Pepper API doesn't expose the local network interface addresses to the plugin, so the plugin has no way of discovering and reporting its local addresses to the server to allow on-LAN P2P.
for cases such as this, RTMP (or RTMFP) fallback to AMS is an alternative, as you have discovered.