Yes, I've tried that and I've tried creating the sequnce myself.
Here is the sequence dragging and dropping onto the New Item button creates:
The audio on the video is compressed and it's stereo on the sequence-- that could be ok, I'm not sure, but it's the only descrepancy I can find between the two and don't know how to change it. None of my Google, lynda.com, or forum searches have brought up anything useful.
Thanks for the input!
The Flip is probably not doing a good job of writing metadata into the files that helps keep synchronization--or it may be doing that just fine, but Premiere can't deal with it. That's sort of the issue when dealing with consumer cameras like this--you can get some unexpected results.
Here's something you might try: download MPEG Streamclip for your operating system (I'm guessing you're on a Mac). Open up one of your MP4s with it, and then select File > Save As. By default, the file type should be set to MP4; leave that and just give it a new name. This is a lossless rewrapping of the file--the video and audio are extracted and the repackaged in a new MP4 container. Try importing that MP4 into Premiere, and check the synchronization.
If that works, I'll give you a clue as to how to batch those so you only have to do it once.