I, myself, haven't got a child with excema but my brother who is now 28 suffered with it for many years.
When he was born he was covered in white gunky stuff(my mums description, not mine!), it was only a couple of months later when she washed him in Johnsons baby lotion, that his excema made its appearance.
We also found out he was allergic to cows milk, so we changed him to goats milk and then changed him to soy milk.
When he was young we lived in Sydney, at the Army Barracks in Holesworthy. We used to go to the beach and collect lots of buckets of salt water to bath him in and mum also says she washed him in oatmeal baths as well.
When he was older he went onto the cortisone creams and that made his excema clear up to the point you can't see it. He still does have attacks but never as bad as what it was when he was younger.

Hope some of that helps

Jess