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.
What do you mean by "pan the studs"? Yes, flex duct is running from the top of the 1200 cfm fan between the studs and outside the house. Its about 8 feet w/ 1 turn at the top. I cannot open the ceiling as the kitchen is above that room.
Also, the square hole left over from the wine cooling unit dumps to a closet in a guest bedroom. So, the fresh air I will be bringing in is not from the outside. Its room temperature air from the guest room.
Not ideal. This small space has been a challenge.