The last thing I would do on such an itinerary is book separate flights to JFK and then to JNB - the risk (especially in the US) of the first flight being late is to great and then the second airline has no obligation to move you to another flight. Does the booking with Jet Blue come on one PNR if not that could, in the event of lateness, prove very expensive.

Looking at ITA the quickest routing is actually via Amsterdam on KLM at 22 hrs 20 mins, the cheapest in Y is booking on United via JFK (which then books you onto SAA as a *A partner).