Don't really have an answer with relation to Flash for you, but considering the wide range of combinations in monitors/video cards/operating systems/personal settings in the world, you will be hard pressed to reproduce the exact color that you see on your own screen no matter what you do. That's just kind of par for the course. Instead, find something that looks best on the most screens you can test on. It won't be perfect, but its the best you'll get.
Generally that is not a problem when coming in with 24 bit sRGB but there have been a couple of recent reports involving Macintoshes. You might search old posts and contact those involved if possible to see if they found a resolution. I don't see it in tech support anywhere.
Was nearly at the end of my rope as well. This was a tough one for me, and all the discussion-board answers were annoying (things like "You can't know what color setting your users will have"). Well guess what—I know what setting I have!
But here is what works . . . instead of using Photoshop's "Save for Web" feature, just do the old "Save As" and select PNG as the format. I did it both ways, using Photoshop's eyedropper both files showed identical color. However, when they are imported into the Flash library, then placed into a Flash layer, then Flash-eyedropped, the colors are different. Very strange, but true.
Very simple solution. Convert the PSD image to 32 bits/channel (under image/mode) and then save. When you import to flash it's good as new.
To work on the image again (do anything with filters or selections, you have to convert back to 16 or below, but then just save as 32 when you're ready to import to Flash.
Not sure why they can't remedy this. I think it's a leftover Macromedia/Adobe glitch.