The simplest way to do it (by far) is to use a socket proxy. The flash application connects to the proxy, the proxy connects to the server and relays streams both ways while logging.

As far as I know, the flash application can only connects to the server where it was donwloaded, so it means you may have to host the flash localy, setting up a little http server.

Take a look at Socket Workbench for an example of a socket proxy. You can also roll your own with java or c#. c++ seems a bit overkill here.