No herbal advice, but I just wanted to put out there that a surprising number of dogs have chicken allergies. If you are feeding chicken, you may want to take a few weeks off from that and see if it helps.
I am quite experienced about dogs. I remember that German shepards tended to skin problems due to pancreatic issues, so you might check. As you mention, i have also always seen that this sort of issue was linked to the food and the digestive system.
You don't say what you cook but avoid whole meal and also sweet and white potatoes. Rice is often good but some dogs are intolerant to it. Any carb should be over cooked in a lot of water that you throw away, including if you use carrots. the best veggies to use are the cucurbitaceae.
Chicken can be a culprit though beef is often more responsible of skin issues. I have seen eczema and itchy skin in dogs fed beef and veggies and some rice, and they were doing doog with a nice fur on chicken carcasses! Maybe also because of the sort of fat and the presence of bones.
On the skin:
Aloe has always been a favorite for me, but I have fresh one due to my climate...
Lavander is useful for local wounds, which means small surface and occasional use.
By far on eczema, the best result I saw was with a tincture of gotu kola. It was always amazing though I was using it only once, as the dog was reacting to the alcohol of course. I got it from the vet actually! Now you find this for humans as an alternative treatment.
Xisca - pics! Dry subtropical Mediterranean - My project However loud I tell it, this is never a truth, only my experience...