I use Dexron III ATF in the primary.
Dexron III ATF.
Along with auto transmissions, Dexron III is also used in chain driven 4x4 transfer cases (NP207, NP208 etc)...
After all, what is in an automatic transmission? Clutches, bearings etc... ATF is also used in chain driven transfer cases (NP 207/NP 208) that have.... chains.
Sounds like a HD primary to me.
Here's what Barnett has to say about primary oil
Barnett Performance Products
As far as what oils to use, we generally suggest following the manufacturer's recommendations. Use only quality motorcycle specific oils. The main purpose of oils in a "wet" clutch application (as far as the clutch pack itself is concerned) is to act as a coolant. Oil flowing through the clutch plates help to keep the plates cooler, resulting in smoother clutch action and longer life. Using too heavy viscosity can cause plates to stick when cold. All Barnett wet clutches are designed to be used with synthetic or petroleum based oils.
NOTE: We do not recommend using the Harley Davidson Formula Plus oil with our clutches. Remember, the single best insurance you can have for your clutch and bike is to keep clean, good quality oil in it!
I use Mobil 1 75w-90 in my transmission.