The Corpus of Contemporary American EnglishCorpus of Contemporary American English has only one entry in its database that uses the phrase "darkest Brooklyn" -- an article in the Spring 1998 issue of American Scholar by Alfred Kazin titled "The art city our fathers built."
I first walked into the Metropolitan Museum seventy-one years ago, as a boy of eleven, led by my father, an immigrant house painter from darkest Brooklyn who liked his firstborn to accompany him as he timidly looked into the city's public places -- the Met, the Brooklyn Museum, the great library on Fifth Avenue, the Aquarium on the Battery, the Staten Island ferry when it charged a nickel. [American Scholar, Spring98, Vol. 67 Issue 2, p17, 10p]
Kazin seems to be using darkest Brooklyn in the sense of Brooklyn's innermost ethnic core, where the gentry dare not tread.