If you call button gradients, rounded corners, etc. advanced shapes then indeed I would go for the Illustrator approach. These are all shapes that translate easily and cheaply into vector graphics/code. For this kind of graphics, vectors are usually much better for memory and performance.
Illustrator can export directly to FXG. Just make sure to tell your designer to anchor his drawings in the top left corner when he does the export so you don't have to deal with offsets.
If however your graphics become more complex (a drawing, or maybe some complex symbol) you're better of embedding it as a bimap graphic.
As a last note: Adobe previously had a product called Catalyst that was supposed to address the designer/developer workflow for Flex apps, but they discontinued it.