Are you looking to do it dynamically? Or are you looking to
put a specific video you see on youtube, into your flash only once?
If you want to do it dynamically, it's a more advanced task.
I know it's possible because there are AIR applications out there
that pull down and save the .flv (flash video file) from
youtube.com by just entering the video ID into the AIR application.
If you want to do it once it's much easier because you can
use the AIR app that I talked about above to pull the .flv down,
and then just implement it yourself via all the various flash video