I have been looking at the British Airways site for info. It seems that the passenger should inform the airline of his conditions especially requiring dialysis. The dialysis per se is not an issue directly but if there are delays then he may need to go to hospital or use a portable dialysis machine. Depending on the other factors, breaking up the trip into 2 with a stopover may make it more tolerable.
You are right to be concerned. He should speak to his doctors as flying is quite stressful on the body, let alone the jetlag etc.
My grandfather was 85 when he decided to visit UK for the first time from Australia. Qantas insisted he got a medical clearance and the doc advised him that he needed a pacemaker fitted to fly. (He grumbled about it but got the pacemaker and had a great trip).
A colleague who had terminal pancreatic cancer was advised that even a short flight would be too much for his body to handle. (our company offered to fly him and his wife in a Hawker 800 for a quick jolly but the docs said no).