I do not know of any ActionScript of Flex specific property
for directly retrieving a user's IP address. Does anyone else know?
However, are you serving your SWFs from a web application
server (PHP, Java, CF, etc)? If so, a sure fire solution is to have
logic in your web application server pull the user's IP address
from the CGI info in the request, and embed it as a FlashVar value
in the HTML wrapper that is being dynamically generated. When the
Flex swf loads, it can then receive the value in the FlashVars.