I've been experimenting with serving Flash files from an Ethernet-based Arduino (you could use an Arduino Ethernet Shield
I wrote a REST-style web API so the Flash app could interact with the device by accessing URLs like this example (which would read the analog value of Analog pin zero): http://192.168.10.1/r/a/0
My goal is to be able to connect to the Arduino board via ethernet and not require anything to be installed other than a browser and Flash.
This example may or may not be helpful to you. :-)