Advantages
Flex is a framework built using ActionScript.
It highly used in making Rich Internet Applications. Its easier to up and running flex applications.
Truly Write Once Run Everywhere and not Write one and Debug Everywhere (javascript surely has this problem, I'd like to get it resolved).
No more browser wars (I support html 5, but that's different).
From Adobe. But its open-source. Flex SDK is open-source.
Runs on mobile devices as well (Flex SDK Hero).
You can use which ever IDE or editor you want. Ant builds are just fine. The problem with all the free editors are no code-hinting. I truly miss that because without code hinting, its difficult with such a huge library. Again we have Eclipse pig (Flash Builder) which you can pay for and other premium IDEs.
The bottom line is its all flash. It suits to both designers and programmers equally. That's why I'm interested in everything flash at the first place. There is not tool in this whole planet which does this kind of seamless integration. I'm a programmer and I have the artistic nature in me as well. So I can program and design all with the same tool.
Good and large libraries.
You could do virtually anything with AS3 (and flex in turn). Yeah! You can even control micro-controllers like Arduino, Phidgets etc all the way to high level stuff like making web sites.
With the upcoming molehill release of the flash player, the 3D realm will kill start to a whole new experience never before seen!!
Disadvantage
Well there aren't much to be thought of. Anyway, the thing is since the framework is huge, the learning curve is more. Cramming everything into your brain will take more time.
The IDEs which actually are required (it will make your life a lot more easier), is really costly.