You will be able to get a credit for the New York and New Jersey taxes you paid on your Kentucky tax return- however, since the New York income is included on the New Jersey tax return, you would not be able to double count the income.
In your case, you may have some of the income double-taxed because you cannot claim a credit for New Jersey, so part will be taxed by NY and NJ with credit to KY. This is an issue because New York has the tax on nonresidents who work for a New York company even if they work in another state under their "convenience of the employer" test.
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