Yech - CorelDRAW EPS import sucks. If you can get hold of a copy of Adobe Illustrator or MM Freehand, try those. Failing that, try Corel.
You may also have some luck with GSView/Ghostscript which has the added advantage it's totally free. Its vector export can be a bit dodgy sometimes though - though it will export nicely to a bunch of common raster formats as well. Does it absolutely have to be a vector object in Flash?
Doesn't HAVE to, but I've yet to master the trace bitmap function. I have this Flash MX Logo thats like 600x600 and no matter what, the edges are rough and the file is like 15-20kb extra. I know a pure vector piece of art would only be 1kb or less.