It appears that Creation always has a pecking order and a food chain. Monkeys, dogs and all pack animals establish an order. THerefore, looking at the natural world would only lead us to believe that slavery was natural and endorsed by reason. Scripture differs, but nature is very Darwinian looking, and slavery fits into this nicely. It seems that natural law would permit slavery.
But I do not put much stock in natural law.
I think Caddy meant "Natural Law" in the opening question of this thread to mean the original manifestation of the Moral Law in creation as many Divines used that terminology. It is confusing terminology since we also call the order we see in nature "the laws of nature."