Here's what I do for my eczema, which my dermatologist recommended after a scratch allergy test came up negative for everything. After your son gets out of the shower, he should pat himself down (not rub, but pat) with a towel so that his skin is still damp but not dripping. Then, if there's a cream that the doctor has given him for his bad spots, put that on. Then rub himself all over with a thin layer of Neutrogena body oil (not sure if this is okay for kids, but baby oil would probably work well too, and it's cheaper) and then top that off with a good-quality unscented lotion. I use the Target brand of Eucerin.
I did this and my eczema pretty much cleared up within a few weeks. I still have some issues on my hands and armpits but everything else has stayed clear.
Also, this might sound gross, but if you can stand the dirt, have him bathe only every other day. Bathing strips the skin of its natural oils and can aggravate a lot of issues. Plus if you scratch skin that's damp from a bath it rips it right open...I know that from experience.
I hope things improve for him!