The oem steel heat exchanger lines are 5/16", same as the fuel supply system. There is no need to use anything other than that in steel. The hydraulic hose material supplied with the typical auxiliary heat exchangers is properly sized to work with the oem fittings/ports.
Unless you are going to add a thermostatic control, the additional heat exchanger should be plumbed in series with the radiator system, just like the instructions recommend. Transmission fluid temps that are "too cool" are just as damaging as "too warm".