I found a Queens' flag online and some information about it.
The flag of the Borough of Queens dates from 1913 and uses the colors of the arms of the first Dutch governour, and a tulip (recalling Dutch origin) within a ring of wampum.
Mark Sensen, 3 June 1998
The tulip symbolizes the Dutch, and the wampum symbolizes the Natives. Also, the tulip is crossed with a rose, which symbolizes the English.
Ferdinand Cesarano, 23 August 2002
In the official seal and flag of Queens County there are a number of symbols that tell a great deal about the beginnings of this County and Borough.
Dutch Governor William Kieft purchased The land comprising Queens County from the Indians. Queens County was created on November 1, 1683 and the territory included present-day Queens County, Nassau County, and part of western Suffolk County. The Governor's Shield is typified by the white and blue stripes in the Queens County Flag.
Two flowers, the tulip and the rose, are surrounded by a circle of wampum, which is taken from the Indian name for Long Island, "Seawanhaka," or "island of sea shells." The first settlers are represented by the two flowers: the tulip, emblematic of the Dutch and the double red and white rose of the English, representing the Houses of York and Lancaster. The Queen's Crown signifies the name of the County and Borough in honor of Queen Catherine of Braganza, wife of Charles II, King of England. The date indicates the year in which Queens County became a part of the City of New York on January 1, 1898.
submitted by: Greg Hofer, 6 July 2001
I couldn't find an image of a flag for Brooklyn. I found emblem on a trash can at Borough Hall, though.
She is a depiction of the strength in unity. That's all I know.