Ah, I think I may know the solution to this problem, it gets asked a fair bit here.
Well, first thing I'd do, make sure to export sounds in audacity as .mp3 to get the best results as they are much smaller in comparison to .wav in file size.
NEXT, put in your sounds in your movie's timeline as you have done before in flash. Make sure that your audio are ALL set to stream or event, it's easier to have them all as just one of those two, but I recommend stream.
Now here's the really important part, follow this:
Go to file>Publish Settings>Audio Stream(If audio is set to stream) Audio Event(if audio is well, set to event).
Now simply change the bit rate to anything higher than the current setting, this feature essentially is what you use to finetune the audioclips' sync with the movie. Keep increasing it until the audio clips sound like they are being heard at the right moments and you should be done!
Hope that helps!