Start with a click track for your song in FL. Allow a four-beat intro or something if it's in 4/4. Record your song, and make a mixdown. Then ship it into FL (the same session you created the click track with). Things should be lined up. (But if you've already recorded the Cool Edit session, then it should be easy enough to insert a click track from FL and line things up right in Cool before carrying out the above procedure.)
It works for me, but it's a cumbersome pain in the ass in two ways: first, it only plays from the beginning, so if I want to work on something at the 2.30 mark, I still have to listen to the whole two and half minutes first. I want a RAM function for this stuff. Second, my computer doesn't like having the two applications open at the same time, so I'm always having to close one out before working on stuff in the other one.
I'm not enough of a techie to know why these obstacles exist, but if somebody came up with a good beats program that allowed me to have it and Cool Edit/Audition open at the same time, and which could access any point in the song in the beats program, I'd pay a lot of money for it. Well, *quite* a bit of money lol.