The itch comes back before the coat does

Skin and coat improve in a fixed order, and knowing the order saves a lot of second guessing. The itch settles first, usually inside a fortnight. The flaking goes next. The coat is last, and it is last for a reason that has nothing to do with the supplement.
Hair grows at its own pace. A dog cannot make an existing coat better, it can only grow a better one, and that takes as long as it takes. What omega 3 changes is the skin underneath: the barrier that holds water in and irritants out, and the inflammatory signalling that makes a dog scratch at something minor.
So if the scratching has eased but the coat still looks thin at week three, that is the expected sequence, not a failure. Give it to the second month before you judge it.
The number to compare is EPA and DHA combined, not fish oil. A gram of oil can carry almost none of either. And oils go off, so a tub that smells sharp has been on a shelf in the light for too long, whatever the label promises.
One caveat we would rather say twice: sudden itching, raw skin, or anything with broken skin and discharge is a vet visit. Fleas, mites and allergies are not fixed by an oil, and a supplement in that situation only delays the appointment.
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