As nobody else has responded I offer my thoughts. Firstly, Flight Engineers are licenced much like pilots after a great deal of training so they are not recruited "off the street" for particular aircraft. Secondly, I imagine that Concorde FEs were well-experienced with some years of expereince on other types before joining the SST fleet.
As has been mentioned many times elsewhere, FEs are a dying breed and the majority of modern commercial aircraft are crewed just with pilots.
If you Google "Flight Engineer qualifications" you'll find enough to read into the dark hours!