The Franklin kite experiment is conventionally dated to June 1752. The standard story: Franklin flew a substantial silk kite into a thunderstorm cloud, ran a wet string from the kite down to a key, drew an electric spark from the key to his hand, and demonstrated that lightning is electrical.
The contemporary documentation is unusually thin. Franklin himself never wrote a first-person account. The substantial principal source is Joseph Priestley’s History of Electricity (1767), written fifteen years later, and Priestley’s account is itself second-hand from Franklin in conversation. Franklin’s own 1752 Pennsylvania Gazette mention is a brief one-paragraph summary describing the experiment as a method rather than as a personal action.
What was actually done
The first confirmed lightning-electricity experiment was performed in May 1752 by the French physicist Thomas-François Dalibard at Marly-la-Ville, north of Paris, using a tall iron rod rather than a kite. Dalibard had read Franklin’s 1751 Experiments and Observations on Electricity and was substantively executing a method Franklin had proposed in print but not personally demonstrated. The Marly experiment unambiguously showed that lightning produces electrical discharge at the rod.
Franklin’s later silk-kite proposal substantively appeared in the Gazette in October 1752 — four months after the supposed June performance, and in language that reads as a forward-looking proposal rather than a backward-looking report.
Modern historians of science (most pointedly Tom Tucker’s 2003 monograph) argue that Franklin may never have actually performed the experiment. The proposal would have been substantively dangerous: a wet kite string is a direct lightning conductor and would have substantially killed the operator. Subsequent attempts to repeat the experiment killed at least one — the Russian physicist Georg Wilhelm Richmann was electrocuted during a similar attempt at St Petersburg in August 1753.
Franklin himself lived to 1790. He never wrote a personal narrative of the kite event. The story took its modern form through the 19th-century American patriotic literature that needed a founding-father scientific moment.