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Ahh. I asked this question a while back.
With converting files to GIF from flash, the quality gets a bit choppy. To minimize this try to use colours from the standard flash palette.
You could also try this method (SarCastiC_RaiN has told me this, i haven't tried it to know the effectiveness):

1.) Create your animation (don't use movieclips that contain animation because they will only show the first frame of the movie clip).
2.) Go to "file" >> "Publish Settings"
3.) On the "Formats" tab, de select everything but .gif
4.) Select the GIF tab and use the following settings:
-Playback: "animated"
-Options: "Optimize colors" and "smooth"
-Transparent: "Opaque"
-Dither: "None"
-Palette type: "Adaptive"
-Max colors: 99999

Note: This will not give you every color, but it will significantly expand your palette. Also, try to avoid the use of gradients because they can often include colors that won't work too well.