Neither the java or Flash client need to be run on the host machine with the Firefly server. To run the Flash client, you do need to have some files on the server. I’m not sure if these are included in some releases of Firefly or if they need to be downloaded separately, but just check the Firefly filesystem for FirePlay.html and FirePlay.swf.
Then open a browser and point to:
http://yourfireflyserverhost:3689/FirePlay.html
For the java client, go to the file menu and select New Library. Enter a name for the library, the firefly host, and port. Unless you changed it, I think the default is 3689.