What about doing raw chicken + base mix (no kibble at all)? The Honest Kitchen's Preference base mix is flax-free and grain-free. Just add chicken or eggs or whatever protein, and some fish oil. One of the things I like about Preference is the dehydrated fruit/veggie ingredients have several natural sources of quercetin, a natural antihistimine. You could also try supplementing quercetin directly, if you think there's a possible allergic component to the itching.
I saw great results giving Natural Eggshell Membrane (NEM) and Hyaluronic Acid/Collagen II with my last oldster. Gatorbytes was the one who turned me onto it. You can get NEM as capsules, or just pull the membranes out of all your eggs. I think you can extract out the HA/Collagen II out of chicken necks and cartilage if you make bone broth.