AN-6 hose diameter is 3/8". Original lines were 5/16. AN6 is the size most builders use for transmission and fuel lines. Be sure not to mount the regulator close to the exhaust like I did. An auxiliary transmission cooler will work just fine for cooling the transmission.
I prefer the plate type. They take up less room and are more robust in their design. You can purchase them with the AN fittings like this one;
https://www.summitracing.com/parts/der-13614