The sideslip indicator in Concorde was used primarily when operating with one or two engines inoperative.
To achieve zero sideslip in the asymmetric case, the climb out would be flown using around 2°-3° bank into the live engines.
This was done to minimise drag and thus maximise aircraft performance.
The gliding fraternity use a piece of cotton, stuck to the outside of the canopy to achieve the same result, but on Concorde it tended to come off in the cruise, so a sideslip indicator it had to be!
Trimming in normal flight was done primarily by moving fuel around, both across the aircraft from wing to wing, as well as the more well known fore and aft transfer.
Ideally, a CG position of 59% MAC was achieved, with zero sideslip, zero rudder deflection and ½° down elevon.
Regards
Bellerophon