The gnarly name kidskin or kid leather refers to leather made from goat or lamb skin— sometimes even kangaroo. It was never a particular brand of leather and we suspect its meaning was adapted at times by advertisers and copywriters to mean any hide that was soft and pliable.
Kid leather has a history in bags, gloves, bookbinding, and of course shoemaking.
Check out more classic shoe ads from my post yesterday on the Apollo anniversary.