Yes they did! Braniff crews operated the Concorde between DFW and IAD, whereupon BA crews would pick up the flight from IAD to LHR, and AF from IAD to CDG.
The service was operated from January 13, 1979, and was terminated in May 1980 due to high costs, and BA's ailing finances.
None of the aircraft were painted in Braniff colors. It was planned, but service was discontinued before that time.
Tom in NO (at MSY)
"The criminal ineptitude makes you furious"-Bruce Springsteen, after seeing firsthand the damage from Hurricane Katrina