I don't know much about flash, but in this respect, regarding outputting to flash, Trapcode Particular works like any other effect in AE so you can turn to Adobe support or try the AE forum at the Creative Cow.
If you want to have a snoweffect in Flash than get one of those
snowflake scripts for Flash (available in all kinds of Flash forums).
Because this is the only way to keep your filesize small. http://www.hotel-saarschleife.de
Here you can see this effect in live.
But if you need a special fx right from Trapcode Particle then
would I recommend to export your animation as png sequence with the
alpha channel turned on. In the second step you can import the
image sequence into a movie clip. You just have to select the first
png file, the rest will be imported automatically. That's all you
have to do.