I doubt there is any way to do this in a Flex based web app. On the server a CGI Variable will contain the IP Address of the machine that made the remote call. But, this could be masked with routers and internal vs external IPs. For example five computers in my home network share the same Internet connection and therefore all use the same IP address. This is a pretty common setup. Getting the names of machines connected to the client would be impossible from the server.
If you're running an AIR app, you may be able to use NativeProcess to execute a program on the client machine to get the information you need. This is way out of scope for what I'd expect to be built in as a Flash Player or AIR API.
I do not know about air, but for flex app, if you are calling server, you can get IP of the machine which is callin the server from the request object in the server (if you are using j2ee in the server).Same for the blazeds.
No argument, but if you read the question (not the subject line) the original poster is asking for very different info. IT sounds like he wants the network names of computers connected to the client machine.
Oops.. did not read it completetly. Probably, something to do with the Applets.
Also, it is not clear on how the machines are connected to this client machine. I mean, is there a server on the client machine? etc.,
I worked on Scanner on the client machine, how they do is, they have a .dll file in the windows folder of the PC, and, there is a library in the Java applet which calls the dll to communicate with the scanner. I've no clue on how the applet calls the dll from the browser. but, I load applet(which is signed) and call the dll, get the data as the image and save it into the server.
Twain is the dll
Morena is the Java applet