The “Gadsden” of “Gadsden Flag” fame is Continental Colonel Christopher Gadsden of South Carolina (and not his grandson James Gadsden of Gadsden Purchase fame). In late 1775 the colonel was a member of the Marine Committee of the Second Continental Congress charged with outfitting the ships of the nascent Continental Navy.
Part of that activity involved coming up with a flag for the navy’s commander-in-chief to fly as his rank flag from the mainmast of his flagship, which they decided would be a yellow flag with a snake and “don’t tread on me” on it. And indeed, Commodore Esek Hopkins used such a flag on his ship, the Alfred. No examples of this flag survived to the present day, so what we have to go on are these words in an entry for 9 February 1776 in the records of the Provincial Congress of South Carolina:
Col. Gadsden presented to the [Provincial] Congress [of SC] an elegant standard, such as is to be used by the commander in chief of the American Navy, being a yellow field, with a lively representation of a rattle-snake in the middle, in the attitude of going to strike, and these words underneath, “Don’t Tread on Me!”
None of this establishes that Col. Gadsden designed Hopkins’ rank flag, though, leaving Whitney Smith (founder of the field of vexillology) decidedly unimpressed:
Because [Col. Gadsden] presented a copy of this flag to the Provincial Congress of South Carolina, it has often, falsely, been called the “Gadsden flag” or the “flag of the South Carolina navy”. [from Smith’s The Flag Book of the United States, 1970, pp. 45-46]
On the other hand, an address by Frederick Cooks Hicks (R-NY) to the US House of Representatives on Flag Day, 1917, and published the next year by the Government Printing Office as The Flag of the United States, says the flag was “designed by Col. Gadsden“. (Was this Hicks’ inference, or did he have some other source? If you know, please comment below!) At any rate, this is now become a commonly held belief, repeated by the Naval History and Heritage Command and many others.
So who did design the Gadsden flag? Like so many vexillological questions of that era, we really don’t know.