I'm with Jerry - Flash's default colorspace is RGB - for print you obviously want to be working with CMYK.
Although usually there's not that much difference between shades when you change colorspaces - I find that it's more pronounced with reds and oranges than with blues and greens.

I would probably try to just copy and paste from Flash to Illustrator - it will stay as vector info and you can adjust your colors from there if you still have problems.

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