Hosting a shared livestream

The company that I'm currently employed at has turned to me to build them a web app that lets them share their YouTube project demos using a livestream service, so that they can all be watching the demos at the same time, (the demos are on a tight schedule, calculated by the length of each of the videos and such)

I've been looking at how flowplayer handles YouTube links and livestreams, but I don't know how to proceed about this.

Another colleague suggested letting the livestream play on a VM and just adding the stream to flowplayer.

Does anyone here know any ways to achieve this, or general ideas?

Thanks in advance!