Cloudflare can most certainly help speed up and protect the site. Sites that do streaming content, however, should move their streaming content to a subdomain we don't proxy in their DNS settings. If you created a subdomain like streams.yourdomain.com, you could then add it in your Cloudflare DNS settings like:
CNAME streams is an alias of domain.com (make sure cloud is grey).
We have seen sites have performance issues because of the number of connections that streamed content causes when running through the Cloudflare proxy.
Note: Embedded services - such as YouTube and Vimeo - would not require any special configuration because that content is being served off of your site.
We did recently introduced Cloudflare Stream (now in beta), a video-on-demand platform for developers and content teams building video applications. Cloudflare Stream combines video storage, encoding, global delivery, and playing into a unified video streaming solution. Learn more here: Cloudflare Stream
For Cloudflare Enterprise customers, we can allow caching/streaming of media as is determined to make sense for that account. If you are interested in learning more about the Enterprise plan, you can contact us through this link: