There are a number of ways to communicate between Flex and PHP but one of the more interesting is over sockets. Socket communication lets developers create near real-time communication by pushing information directly to the client. In this article you'll see the basics of how to use PHP as the socket server and connect it to a Flex application.
Using direct socket connections, the client and server communicate directly over a port and any data can be easily passed back and forth over it. This method requires that you set up a policy file for the application for security reasons before it can communicate with the PHP backend. With this in place, the rest is easy. They include the PHP code you'll need to make the socket request handler and how to return a response that the Flex application can read. Code for the Flex application side of things is included as well - a simple application that grabs a "stock price" and plots it on a graph (seen here).