As far as I'm aware of, the Flip video camera should have a built-in microphone.
I can confirm that some MP3 players can record as well as play. You'll need to check the specifications, as most don't clearly state so apart from in their specifications.
Another option would be to get a Dictaphone that records to a flash card or which can be connected to a PC. These tend to have better recording quality than an MP3 mic as well as a dedicated record button.