Somewhere recently I read someone saying that they booked with Kulula but noticed that they flew on a Comair BA aircraft - a standard BA flight with full BA service. Very odd, I thought.
In looking up some SA domestics for my partner this week, I noticed that indeed there are some flights offered on the Kulula website's booking page that aren't actually Kulula-branded flights but BA-branded flights. These don't match any flights appearing in the Kulula timetable, but do match exactly - including flight number and all - with Comair's BA-coded flights. So, clearly, Kulula are just selling tickets for some of the BA-branded flights.
It looks like the ones to go for are the four digit flight numbers - these seem to be the BA flights. The three digit flight numbers are the Kulula flights.
But I can't guarantee that it'll save you any money over booking the BA code, and I suppose you won't get any FF points or benefits.