E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
To fly the kite is to raise the wind, or obtain money on bills, whether good or bad. It is a Stock Exchange phrase, and means as a kite flutters in the air by reason of its lightness, and is a mere toy, so these bills fly about, but are light and worthless. (See STOCK EXCHANGE SLANG.)