Is there any credible evidence that Benjamin Franklin actually did his famous kite experiment?
There is Frankin's letter of Oct 1 1752 saying that the kite experiment was performed successfully in Philadelphia, which was read to and published in the Philosophical Transactions of the Royal Society a few months later.
There is also Joseph Priestly's The history and present state of electricity (written about 15 years later after discussions with Franklin) which provides slightly more detail including the involvement of Franklin's son. Apparently the kite was not struck by lightning but still carried a charge from the thunderstorm.
This does not preclude Franklin from having invented the whole thing, written a letter about it and lied to Priestly, and then persuading his son (later the British Governor of New Jersey) not to disown the comments, but it does makes it more likely that the experiment actually happened.