The swf exporter tries to convert to Vector (like FlixPro) which of course gives you that awful look.

I actually export the character to images (png so background doesnt repeat/show and create large pic sizes) then I bring all png into Animation Shop from Jasc. Then crop the figure frames as tightly as possible. Then select all frames - export frames to pngs. This usually drops the size of the pngs drastically.

Then I import character movement pngs as a movie in flash and throw in the background, etc. Keeps swf files fairly small by not continually repeating non moving/changing items.

For example - if you are having a character walk across the screen - you would only need the left and right walk segments in png then bring them into Flash and have it continually loop while you move the character from one end of screen to other.

So far this has worked best for me and I have tried many different ways (specially since some animations per character are over 750 frames when talking!).

Maybe someone else has a better way of keepiing quality while importing to flash - if so would love to learn as my way does choke up a lot of disk space.