ONLY Air France and British Airways owned the Concorde, whereas Singapore airlines operated the above mentioned joint venture flights together with British Airways (1976-1980), one side painted in BA colours, the other in SQ colours.
Furthermore, Braniff signed for some Concordes with Aerospatiale/BAC, however, this contract was cancelled later on. Worth to mention, anyway, that Braniff (prematurely) printed airline postcards showing photo montage pictures of "the Braniff Concorde" due to commence services...! This never took place. By the way, Singapore Airlines issued several airline postcards of the Concorde as well.
Another colour scheme applied to Concorde was that special Pepsi promotion tour aircraft.
That's it. Hope this helps.