Lee Brimelow has a tutorial here for building your own video player in AS3, this should help to get you started - though from the way you're talking about it I get the sense that you're not really a flash developer, you just have to work with flash for this project - so what you're asking for may be a little more complex than you expect.
First watch this:
http://gotoandlearn.com/play?id=46
Then understand that when you build a player it fires certain "events" at certain times. Like kajyr above says, you need to listen for a specific event that tells you that the current clip is over. When that even fires, you have to tell your player to play the next clip.
What you're asking for is entirely possible and even easy if you understand the basics behind it. I built a tool that handles dynamic playlisting etc at my old job and it only took about a day to give it every feature we needed. But you do need to understand how AS3 works in order to make this work.
Alternately you may be able to find some sort of video sequencing app at http://activeden.net/ - they have a lot of pre-built flash components and that's another way to go.