When Adobe bought Macromedia, many workflow problems were resolved. Others were not, you cannot copy artwork in flash and paste it into illustrator and achieve desirable results. The vector data behaves in strange manners and becomes jagged. Furthermore if you select export to .Ai in flash and open in illustrator the colors shift when opened (even when going RGB to RGB).

The work-around goes like this:

1. In Flash, go File -> Export ->Image…. Select .Ai.  Open the file.
2. Copy and Paste the same artwork from Flash to Illustrator.
3. Select all the elements which are one color (For example the teal leaves/tree trunk) and then use the Eyedropper Tool (I) and click the copy that has the correct color.
4. Repeat Step 3 for all other colors (For example the lettering)