if you saw a picture of a Sopwith camel with a Red-Blue-White cockade, I would suggest that it belonged to the US Navy. If you can get hold of the Profile Publication for the Camel, it illustrates an F1 Camel flown off the USS Texas, circa 1919.
British cockades were usually Blue-white-red, however, R.N.A.S. aircraft used a lighter shade of blue than RFC and RAF aircraft. The real exception to this, was in the case of home defence night fighters where the white part of the cockade was painted over in a dark colour - usually illustrated in colour profiles as a very dark blue, so the night fighter cockade was Blue-dark Blue-red.