I use palm oil in my recipe. But generally, palm oil alone do not really have any great benefits to the skin. The use of palm oil is to stablise other oils in the soap so that the structure will stay.
I have not use palm kernel myself. but in some books, they describe palm kernel as a moisturising oil suitable to be used even on baby skin. in addition, as it also produce bubbles, it can be use as replace of coconut oil sometimes. However, I would think that its best to test it on yourself as each individual skin is different as there are also books mentioning palm kernel as drying.