Funny after I posted that there was a thing about those not working on TV last night, watch Dog I think, saying they show up what you have recently eaten, & not what you are intolerant too
, they also had a specialist confirm that there is no reliable test to show up intolerance, only allergies, & only exclusion diets & diaries will work for that.
& Ignore my dairy allergy bit
sorry I'm getting muddled in who I'm replying to, you didn't mention stool problems 
I should of added though ,,,have you tried adding Epsom Salts, Oats & Lavender oil to his bath, they can all really help with soothing sore skin, & helping relax him so that the stress of having it, doesn't add to the stress that makes it worse, if that makes sense
.......the oats can be messy, but he'll probably really enjoy rubbing handfuls on his skin in the bath, & it is really soothing & healing.
Also there is a cream, Zambesie Botanicus (or something similar) also known as Sausage Tree, its a green tube, & you can get it from good herbalists & health food shops, it is a natural steroid cream, so still needs a bit of care, but as its natural it is better & I found it very effective for flare ups, more so than anything the GP gave, a friends Daughter has true Excema, & she swears by the stuff,