Transmission cooling line fitting size help

Thanks, I am close to having the plumbing completed with rubber hose. Just need the one fitting and this part will be completed. Is the fitting 5/16th flare (which seems right) or 3/8s flare which seems to big

I did plan to upgrade to braided later - since I would know the lengths. And bending line would be really hard for cooler location - and probably beyond my skill and patiences

I decided to mount the cooler on brackets in front of the radiator and route the 3/8s hose through existing holes - the routing has nice gradual bends and I think is pretty nice.

I am so close to getting the car back on the road