Many moons ago BA used to fly as a scheduled route Dhahran - Bahrain. Very quick.
I have the Dhahran-Bahrain sector in my logbook (1976). Unfortunately I only recorded the 'chock-to-chock' time, which was 25 minutes, so can't remember the flight time.
Another short sector was Montego Bay to Kingston. Only a short distance but longer flight time as you had to climb higher to get over the hills.
Dave