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Kid Rock is very proud of his otter skin jacket, not because it's warm and luxurious ... but because it's a big F-U to the animal activists ... including his ex, Pam Anderson.

Kid was at Uncle Jack's Steakhouse in New York City Tuesday night, celebrating the release of his new album, when he decided to brag about his coat ... completely unprompted.

It's clear he's very fond of the jacket -- which he had monogrammed with a ridiculous pun -- but the whole exchange seemed purposely orchestrated to irk his animal-loving former flame.