Go fly a kite

There are two possible theories for this expression. 

One of them centers around the stock market crash of 1929. In American English, from 1805 phrase fly a kite "raise money by issuing commercial paper on nonexistent funds;" According to The Toronto Star -- April 4, 1993, Sunday, FINAL EDITION: The phrase - loosely meaning go do something futile - originated during the stock market crash of 1929. It referred to "the useless bits of paper being tossed out the window" after the crash, she explains.

The other theory is attested by 1942, American English, probably tracing to the popular song of the same name (lyrics by Johnny Burke), sung by Bing Crosby in "The Star Maker" (1939):

Go fly a kite and tie your troubles to the tail 

They'll be blown away by a merry gale, 

Go fly a kite and toss your worries to the wind 

And they won't come back, they'll be too chagrined.

(for sources click here and here)

Today it basically means - in the very British way of saying it - bugger off. Or as us Americans would say, get out of my sight.