Hi Andy,
First of all, what is Frameworks - could you please point me to their website and so I could see their documentation? I myself mostly work with core web backend coding (PHP, mySQL) and frontend (HTML, CSS, javascript and image processing), without help of any website builder (framework) e.g. Bootstrap, jQuery, Wordpress, and so on.
Secondly, I think the most important thing is to have the MP4 version of your FLV videos. A couple of years back, WEBM version is required too (for older browsers), but now I guess MP4 is sufficient (for modern mobile / desktop browsers).
The player itself is not too important. I could see that right now you're using Flowplayer, but there're few good player you could use out there.... or else build your own player with HTML5. I myself is with the latter :)
Third, your web pages need to be updated too. All parts inside those pages seem to be too small to be viewed on small mobile screens. Right? But I guess this is not too important at the moment.
Am looking forward for a little discussion, so I may come up with an idea of where to start.
Warm regards,
Hendra D.