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"Go fly a kite" is an idiom that is used to tell someone to go away because they are annoying or have done or said something irritating. The phrase is no longer commonly used. It was believed to have first arose in the 1940s, when it was popular on shows and other forms of entertainment for a few decades. The phrase may have originated from its literal meaning: if person were to go fly a kite, they would have to walk away to do so.
Farlex. (2015). Go fly a kite! In The Free Dictionary's Farlex Dictionary of Idioms. https://idioms.thefreedictionary.com/Go+fly+a+kite!
Writing Explained. (n.d.). What does go fly a kite mean? https://writingexplained.org/idiom-dictionary/go-fly-a-kite