I know you are looking for good solid specific answers, but its not really that easy. there are so many supplements ect out there, that its easy to get lost in the jungle. If I were you, i would get a book, Timeless Secrets of Health and Rejuvenation, by Andreas Moritz who has a forum here at curezone. Follow the cleansing, eating and general health advice as best you can. This would include liverflushing, colon cleansing and kidney cleansing... from there you add a few specific supplements for eczema.
Kefir (homemade) if he can tolerate it, cod liver oil (if not allergic)... evenprimrose oil, minerals... these are good places to start.