Rapturous applause, or three times three and one more. The expression originated with Lord Winchelsea, who proposed the health of the Earl of Roden, on August 15th, 1834, and added, “Let it be given with the `Kentish Fire.' ” In proposing another toast he asked permission to bring his “Kentish Artillery” again into action. Chambers, in his Encyclopædia, says it arose from the protracted cheers given in Kent to the No-Popery orators in 1828-1829.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894