We find that the fastest way to bring files from Illustrator into Flash is just copy and paste them from one app into another, but… Flash MX has some issues with this method. Majority of pasted content that contains text, when pasted into Flash MX from Illustrator becomes corrupted.

So, one way to overcome this problem is to save Illustrator file in EPS format and import that EPS in Flash MX, a bit of a long process, if you consider all the steps it takes: In Illustrator choose save from menu, name file, click OK, then in Flash MX: choose Import from menu, browse to the file, select it, click OK.

Not a bad method at all, but if you have Flash 5 still installed on your computer, you can bring your content with text from Illustrator to Flash MX faster with just copying and pasting.

When working with files between Illustrator and Flash MX, we always keep Flash 5 open as well, and after copying our content from Illustrator we paste it into Flash 5 first – it pastes good 100% of the time, then straight away we copy the content from Flash 5 and paste it in Flash MX, and you’ve guessed it - it pastes good
100% of the time.

Again for us this method is faster then Export/Import way.
And if you still have good old Flash 5 – install it
and give it a go.