afaik:
flex builder is not free. the flex sdk is. flashdevelop is free (windows only)
flex builder doesn't do vector layout or timeline-based animation.
you would still need flash ide to create the sprites and do some of the animation (depending on the complexity).
these could then be linked into the mxml via swc/swf.
flex is strong at mxml (ria widgets) and as3 code.
if you wanted to port it to air, you could do that but then you'd need an air wrapper if you wanted to package it to be self-executable.
i'm not a big fan of the air runtime. i prefer standalone executable code. but the benefit of using flex would that it could be compiled to swf for web use as well.