I dont have my BackTrack stick with me at the moment so I cant check, but I think VLC media player is installed so you should be able to use this to play videos.

Also if you are using the live cd you will not be able to install more apps in realtime, you will have to add them to the cd image.
You might want to move to a USB version, then you can use persistant mode to make changes.

If this doesnt help you might want to post a link to the video if its online and we can have a look see how we can help.

Might want to open a Shell and go:

wget http://fpdownload.macromedia.com/get/flashplayer/current/install_flash_player_9_linux.tar.gz

tar -zxvf install_flash_player_9_linux.tar.gz

cd install_flash_player_9_linux

./flashplayer-installer

Goodluck, let us know if that works.