What impact did the Concorde have on business of other sub-sonic airliners?
A few thoughts:


The British Airways Concordes only operated scheduled on the London Heathrow- New York JFK route. This implies this is the route under the most competition. There has been enough pressure on this route even after the demise of the Concorde for several companies (as well as BA) to try business-only services on this route.
By experience, changing flights is never quick in the US since you need to go through customs and add time margin to ensure you make the connection (Think three hours connection time on the ground). I think even before the current security state you'd rather have taken a direct flight than change from a Concorde to a domestic flight if possible.
I don't think the charter destinations would have caused much impact on other airline operations.