as i understand he is flying out LAX Los Angeles , your best bet considering more the comfort level for your father , just take the newly introduced flight from Los Angeles to Istanbul ( which is the longest leg) and than connecting service Istanbul -Cairo about 2 hrs flight all on TK Turkish Airlines. It is the most direct flight.The less flights he changes the better it is. and TK has quite improved service in J class I would say very pleasant and since it is a new service might find offers and more availability if travelling on miles.