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Hi, Welcome to Just Answer. You're through to Dr Chris, a Vet based in the UK. I am reviewing your question and will get back to you shortly.
Coconut oil should not be harmful in small doses but can cause upset stomach in some cats.
You may find that an omega 3+6 and Vitamin E supplement such as Yumega for cats may be more effective for your cat, see https://www.amazon.co.uk/Lintbells-YuMEGA-Skin-Coat-Supplement/dp/B001ALEGYE
Failing that a visit to the vets will be required that the skin and coat changes are not due to another underlying health condition.
I hope that answers your question? Please let me know if you need any further help or advice.