Instead of spending a month on digesting a heavy Flex programming book with 500+ pages, you might get a better understanding through a good video course in a couple of hours.

Here are some places I highly recommend you to start with:

• Adobe Developer Connection: Flex Video Training
  The official Flex training video from Adobe. It contains 26 videos that cover important topics such as: Flex Basics, Component Development, Backend Integration, Visual Effect, and System Architecture. The best part is, Adobe puts those courses into 5 days learning schedule (2 hours per day). So you can quickly grab the essential Flex skills in a week.

• Flex 4 Beta in a Week
  Want to get ahead of the game? Then this is the one you really can not miss. Although Adobe has not released Flex 4 yet, it already provides this fantastic video training online. By downloading a Flash Builder and following all the exercises, you will soon become a Flex 4 expert in many people’s eyes.

• Flex 4 SDK and Flash Builder 4 Beta Preview
  This is a 1 hour 41 minutes video tutorial provided by the top online training company – lynda.com. In the course, the Adobe Certified Instructor David Gassner will give you a quick tour of Flash Builder 4 and how to use new Flex 4 features (e.g. Spark text control).

• Flex 3 Beyond the Basics
  This an intermediate level Flex video training also from lynda.com. You will get to know many advanced skills such as Cooperating Flash with Flex, Customizing Component Skins, Building Animations, and Using Flex in ASP.NET or PHP.
  

One thing I want to point out is: you do need to pay a fee ($25/Month) to watch those trainings from lynda.com. However,  it provides you unlimited access to over 700 video courses such as Flash, Java, AJAX, Ruby on Rail… It is truly a great online training library for all programmers and designers.

==> Click here to find out more about Lynda.com