My Requirements are similar to this old question of 2009. I am just re-posting since OP is kind of 2 years old and the question is closed now.
How can I tra
You can send data directly to a remote machine; yet, that machine would need to be listening, and unless you are using Air, that machine would need a socket policy file. Obviously not being able to connect multiple machines directly to each other without a policy file, forces you to have a central server, and prevents straight forward implementations of in browser p2p chat/video/(w/e) applications.
So you have to have a central server; however, you don't have to pay for one.
I knew I had read about this somewhere, so I searched google and came up with the links below.
http://haxe.org/doc/flash/peer2peer
https://github.com/OpenRTMFP/Cumulus
All you need is a developer key, that Adobe gives away for free at:
https://www.adobe.com/cfusion/entitlement/index.cfm?e=stratus
With the above being said, you will need to know some c++, in order to take proper advantage of this.
If you want to learn how to do something basic to get you started, and you are really just interested in developing something for your local network, then these articles tell you how to do RTMFP as a multicast Group:
http://www.flashrealtime.com/videotutorial-remote-device-controller/
http://www.flashrealtime.com/local-flash-peer-to-peer-communication-over-lan-without-cirrus/
[EDIT: the content for the last two links, as the site removed those pages, can currently be found using the waybackmachine and the snapshots around early 2011]
There is a ton of stuff that you can do with the information above; yet, I would start small.
You will need anyway a media server, either FMS or SmartFox or else and have both parties connecting to the server. It will also be dealing with the encoding. I don't think you can do that without a media server in between...