Give him good source of probiotics - I highly recommend lactobacillus sporogenes, these are quite resistant and have high success of implant (Flora Balance, complete probiotics, latero-flora).
Probiotics are required to produce B-vitamins, vitamin K, Biotin; Biotin is critical for fatty acid metabolism so a compromised bowel flora will result in nutritional deficiencies which will eventually lead to topical conditions like eczema.
If condition is severe you may want to add oil of oregano to purge some unwanted pathogens and supplement with food based B-vitamins (specially biotin) and EFAs. I would caution overusage of flax seed as an excess of omega 3s can exarcebate condition. You may want to try a 4:1 omega 6 to 3 ratio (the perfect ratio) with something like E-lyte blend (sunflower seed oil/flax seed oil). Don't forget saturated fats are needed as well.
Being so young, his likes/dislikes to natural foods may guide you on proper diet