Could the agent be looking for the flight you want under a codeshare (DL) flight number? Not all intraEU KLM flights carry DL flight numbers, just the ones that will be more likely to be used as connections to/from DL flights. You could look up the flight number, not just the time, on the KLM website and try calling DL again, this time telling the agent the flight you want with the flight number rather than the time.