It's very simple, Flex is intended for developers while the Flash Authoring
Tool is meant for designers. Even if you design pure AS3 projects Flex now
Flash Builder will be the tool of your choice. Also the Flex SDK offers a
great set of pre-built components to speed up your projects.
Flash is great for creating timeline based animations. Flex is great for creating event based applications.
You could do animations in Flex, and you could do applications in Flash, but you'll be better off in the tool that best suits the purpose.
Flash will continue to be hugely popular, but as more people leave Flash for building applications, and as the RIA (Rich Internet Application) space realizes its full potential in the next 3 - 5 years, Flex / AIR should become hugely popular, and thus expertise in these areas will be lucrative.
Some people ask what book to use in learning Flex. I always say use the Flex Builder help system. I read 3/5 of the help system twice, and have passed the Flex 2 and Flex 3 ACE exams.
This link is just the introductory material, but it will give you an initial understanding of the key constructs in Flex.
Continue after this section in the help system.
If this post answered your question or helped, please mark it as such.