No. vaseline may help moisturize the skin, but it will not cure it. There is no current cure for eczema, but there are other treatments and some work better than others.

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Vitamins alone won't provide cure but will aid cure.

Vitamin E

You can cure a dog's eczema by applying lavender oil and aloe to it's ears. Both of these products will help heal and rebuild the skin cells of the ear.

Steroid ear drops. That is all I know of. Looking for more.