He is no burner of navigable rivers; i.e. he is no conjuror, or man of extraordinary abilities; or rather, he is but a simple fellow. See Thames.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Burner * BurntNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes