Not a vet so not sure I can post there but I've learned quite a bit about food allergies while working in the pet industry for about 13 years (grooming, pet retail, vet clinics). I would give it 2-3 months once you have completely transitioned foods. I was taught early on it can take up to 90 days for a food allergy to completely leave the body. Good choice with moving away from chicken as a protein, it's becoming a common allergen for pets. Also, are you using a probiotic? Improving healthy gut flora can go a long way with skin issues and reducing allergies. Dogs and cats get the same benefits from probiotics as humans do.

If you want to get a little more in depth playing with foods you could look into the Chinese philosophy behind warm, cool, and neutral meats/foods. Feeding a cooling meat or foods might help reduce skin issues/irritation/inflammation.

Best of luck with everything. Allergies, especially food allergies, can be an absolute bitch to deal with. I've seen things that work and help over the years but every animal responds differently.