ACV may reduce yeast numbers a little if present, but it is irritating due to it's acidity and can be drying which will further add to skin itchiness.
If surface bacteria are present you may do better to use Dakin's solution to reduce bacteria, but managing allergic skin changes requires more than just reducing surface organisms.
Here is a link with information about how to make Dakin's solution. LINK HERE
Treatment for all animals with allergic dermatitis should include:
1. Bathing and clipping the hair coat to a short length which helps to decrease exposure and contact to environmental triggers. Bathing with appropriate veterinary shampoos will not dry out the skin and follow up with a humectant like Humilac® to protect skin moisture: Humilac
2. Restore the skin's barrier function with nutrients and topical products. A few of the newest topical products that show promise are:
1) Dermoscent® - helps to restore the lipid layer of the skin and helps to maintain it's hydration and normal skin defenses against allergens, especially the barrier function. See link: Dermoscent.
2) Allerderm Spot On® - help repair and restore the epidermal (skin) barrier in canine and feline patients suffering from skin disease. See link: Allerderm spot on
3) Sogeval® DOUXO® Seborrhea Spot-on - helps to restructure the epidermal barrier and control inflammation. See link: Douxo Spot on
Hope that helps.