It is my understanding that when they arrived from BIO there was a massive queue to transfer from T3-T5 and even with the Fast-Track they where unable to make it to the flight to JFK. They were then rebooked onto a flight to ORD and then on UA (poor them!) to SFO. Unfortunately, when they arrived at ORD their flight to SFO was cancelled (I do not know the reason. How can one find it out?). So I was wondering what if any compensation are they due?
I don't think this is looking good for you. If UA cancelled the flight - and assuming BA didn't know about it at the time of rebooking - then it's down to UA to provide compensation. Now this is where it gets finicky. The courts have now ruled that airlines are responsible for non European connecting flights, however American airlines have so far resisted taking on this liability. I suspect over time that will happen, but as things stand your claim is against UA, not BA, and I've no idea how UA will respond to a claim. Now there isn't enough information to be sure about other approaches, since I'm not sure if it's BA or AA going to ORD and / or any delay on BIO-LHR. If it was Thursday's flight then that got into LHR at 13:06 on a schedule of 13:00. But looking at this by all means try claiming against UA but you may be looking at a customer service gesture there. If there are any right to care aspects, then you could still look to BA if UA decline.
Off the topic of EC261, it's disappointing that the T3 to T5 connection didn't work well for your relatives, though yesterday was a very busy day for LHR. I guess a 6 minute delay didn't help either. I'm surprised BA didn't find another JFK service but there again I imagine they couldn't find onward seats on AA late on. In that situation I would probably have asked to go JFK-LAX-SFO rather than accept United. But hindsight is marvellous.