Hair loss and dry, flaky skin, as you describe, can be cause by various conditions. External parasites like fleas and mites could be responsible for the hair loss, even if you don't see any fleas or your cat is not an outdoor cat. Humans can bring fleas into the house on shoes/clothing. Hair loss can also be attributed to a fungal skin infection called ringworm, which has nothing to do with a worm at all. Here is more information:
Ringworm can also cause dry, scaly patches which may or may not be itchy.
If this is ringworm, an over the counter anti-fungal cream, like Lotrimin AF may help, but it is harmful if ingested, so your next best step would be to bring your kitty to the vet for an in-person evaluation and he can be tested for ringworm with a special light called a 'Woods Lamp,' which is like a blacklight. The ringworm spores will be irridescent under the light, if present.
Hair loss and dry, scaly skin might also be related to skin allergies that may be caused by environmental and/or food issues. Many cats are allergic to poultry, so some manufacturers make 'limited ingredient diets' for these cats, which contain novel proteins and carbs. Royal Canin, Natural Balance, Blue and many others make these kinds of foods with duck and green pea, venison and brown rice, and many other varieties.
Some over the counter sprays and lotions can also help with these allergies if your cat is itchy and/or needs to restore moisture and Drs. Foster and Smith make some good ones.
Adding more Omega 3's to your cat's diet can also be helpful. You can add Wild Alaskan Salmon Oil that comes in a pump bottle, right on your cat's wet or dry food:
Bring your cat to the vet for a definite diagnosis and treatment and I hope all will be well!
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