As the Zend Developer Zone points out Mihai Corlan of Adobe has written up a lengthy tutorial about Flex, specifically targeted towards PHP developers.

I want to share with you some of the things that are specific to Flex in relation to PHP. At the same time I want to introduce Flex by comparing it with PHP whenever this comparison makes sense. Thus this article is for: PHP developers that want to learn more about Flex and Action Script 3 than a simple definition can provide [or] developers that have already made their first attempt at coding a Flex application and want a broader, deeper understanding.

The tutorial starts from the basics for those not acquainted - what is flex, why you should care about it - and moves quickly through MXML, Actionscript3 and examples with each. He includes an example showing a simple user authentication script and how to interface that with a PHP backend.