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You can copy paste modified parts of your artwork from Illustrator to Flash. Here's more information:
Please let me know if you have more questions.
Thanks for the reply Suhas.
I guess the answer to my question is that there is no good way. In the photoshop/illustrator workflow, I can paste a document from illustrator into photoshop and then double-click it in photoshop to open it back up in illustrator and edit the original. I have seen posts on people doing this between Flash and Illustrator with the now-discontinued Flash Catalyst- a process that was apparently called round-tripping. Ideally, this is the functionality I'd like to have between Flash and Illustrator but I take it from your reply that the answer is 'Does not exist.'