The buttons illustrated are not consistent with know documents and examples regarding British Royal Navy buttons. They were introduced by an order of 29 July 1774: "...the Buttons to be flat, with an Anchor and Cable engraved thereon...". Thereafter, the Cable is always shown. In 1812, the Crown is added above (Dudley Jarret, "British Naval Dress", London, 1960). None of the examples, be they British, American or French, illustrated in Don Troiaani's "Military Buttons of the American Revolution" (Gettysburgh, 2001) are like those illustrated in your querry.
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