Flex is for data, Flash is for graphics. (I haven't tried Flex.)

You're going to need a way to create the graphical assets for your application, and as far as I know that means Flash - especially if you want vector graphics.

The Flex SDK is free, but you have to pay for the GUI builder.

I tried going "completely" open-source last year for a project with the FAMES (osflash.org) stack. It was a pain, but it had its benefits (mainly an actual IDE). It was still just for ActionScript, too - need flash for any kind of remotely complex graphics.

You can do some programmatic drawing in Flex, but for the most part you need to load in external graphics. Flash is one tool for making (vector) graphics, but you could make them in Photoshop/GIMP.

I use Flex, and it's more intuitive than Flash if you're used to OOP and IDEs (and not used to the timeline), but it probably lacks some graphical capabilities for game programming.