Just using a Plugin on a tab you can see here that you can stream youtube videos. Just add a Plugin to a tab. Then enter the youtube video page url, and it works.
So, you can stream video from a webpage into TouchBuddy. It is possible. You will have to figure out exactly how to do it they way you want for your profile. I don't know what you want. But if you want a custom page to do just exactly what you want, you will have to figure that out yourself..
Good Luck.