You want the path: (fresh air) -> (machines) -> (outside) to be as wide and have as few turns as possible, while still being fairly direct.
Is dumping the heat into a "receptacle" and then bringing it out going to be a wide open path, or will it just let the heat pool up?
Why not let the entire room be a "duct"?
Is the flex duct running between studs?  If so can you just pan the studs so the channel forms a natural "duct"?
What's above this room?  Attic? Perhaps you could open the entire ceiling, extend wall up and over, and put gable fans on side of house.