Small combustible bodies blazing at one end and floating in a glass of liquor. The liquor was stirred about with a candle-end to promote combustion. A skilful toper would swallow them blazing, as we swallow the blazing raisins of snap-dragons.
“He drinks off candles' ends for flap-dragons.” —Shakespeare: 2 Henry IV., ii. 4.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Flap-dragons from Infoplease: