our child had it as well, in the end we found out how to get rid of it by mistake. The kids (all 4) got lice, one of the home remedies for lice is coconut oil left on the head for many hours then combing. Basically the oil soaked into the cradle cap and when we did the combing large chunks came off. The lice comb is pointy so it got under the cradle cap, and the long soaking had softened it all.

If we ever had that problem again i'd cover the head with coconut oil, put on a shower cap and in 4 hours gently pick at it with a comb. I imagine other oils work as well. I have no idea if this is good advice, just know what i saw ;) oh, and i should mention wear old clothes, they get oil on them :(