Chapter 29 of “Developing Macromedia ColdFusion MX Applications with ColdFusion Markup Language” (download pdf / all CFMX docs) contains documentation on using Flash Remoting with ColdFusion MX.
Since we haven’t officially announced other versions of Flash Remoting, we don’t currently have any documentation publicly available on using Flash Remoting with non ColdFusion implementations. (stay tuned.)
Note : Make sure to read through the other posts here as i have put up a couple of examples of using Flash Remoting with web services, ColdFusion, and ServerSide ActionScript.
Finally, if you have a question on Flash Remoting, you can post them here.
Update : If you have installed the Flash Remoting Components, you can also access the documentation from within Flash MX via (Help > Welcome to Flash Remoting) and (Window > Reference).