Like the position of Navigator, they were made obsolete by greater automation, full authority digital engine control (FADEC), and similar technological advances.
Rebalancing fuel tanks was a major thing in Concorde indeed. I don't remember details exactly, but to maintain the supersonic speed, Concorde needed to be in a certain position, and to maintain that position, fuel would have to be rebalanced regularly.
If you really want the technical details;
1) Flight Engineer - https://en.wikipedia.org/wiki/Flight_engineer
2) Concorde specific (see Technical Section) - https://www.heritageconcorde.com/
3) Concorde Center Mid Engineer's Panel - https://www.heritageconcorde.com/mid-mid-engineers-panel
4) Concorde from the Engineer's seat (another Flight Engineer) - https://www.britairliners.org/airliners-article?title=from-t...