This borough of New York City lives in the shadow of Manhattan, both in the world of cocktails and in popular consciousness. In terms of physical size and population, Brooklyn is actually larger than Manhattan. Like the borough for which it is named, there's a lot going on in the Brooklyn cocktail.
Combine in a shaker with ice, stir with the intensity that you'd have if you perpetually lived in someone else's shadow, and strain into a chilled glass.
Why kings and Dem Bums? Brooklyn is Kings County. Dem Bums is a moniker that referred to the Brooklyn Dodgers baseball team, which moved to Los Angeles in 1957. Some people who grew up in Brooklyn, e.g. my father in law, still despise the move. The etymology of the name comes from Brooklyn pedestrians' ability to evade trolley streetcars -- the Trolley Dodgers.
Over the years there have been many variations of the Brooklyn. I selected this one because I like rye and it's easy to obtain the ingredients. Have enough Brooklyns, and I can sell you the Brooklyn Bridge.