From the fairway, the only place on St. Andrews that I can think where I would use a flop is the 5th hole, front pin location, and just off the green in front. Everywhere else, I would use either punch, pitch, or choked-down full shot.
Well, maybe I might use it just off the green of the 14th hole as well (again front hole location). Still, in both cases, I would use it considerably less than 100% of the time.
In my opinion, the pitch and punch shots are the most consistent shots in the game. WalkofLife's 50-yard punch chart is fantastic.