The Flag of The Bronx, comprising a 17th century Dutch flag with the seal of Jonas Bronck, the borough's namesake superimposed upon it. The American (golden) eagle sitting atop the hemisphere is believed to be facing east to indicate homage to the Old World, while the banner reads the latin "ne cede malis" meaning "yield not to evil things".
The flags design was adopted by the borough in an unofficial capacity in March of 1912, while the alderman of New York officially codified the design on June 29, 1915. The legislation officiating the flag reads as follows-


No. 1959. An Ordinance Amending Chapter 1 of the Code of Ordinances by Adding a New Section, Numbered 3a, Relating to the Official Flag of the Borough of The Bronx.
By the Alderman of The Bronx—

Be it ordained by the Board of Aldermen of the City of New York as follows:
Section 1. Chapter 1 of the Code of Ordinances of the City of New York is hereby amended by adding thereto a new section, numbered 3a to read as follows:
"Section 3a. The following design which has been in use in the Borough of The Bronx since March, 1912, is hereby adopted as the design of the official flag of the Borough of The Bronx to wit:
"Flag containing the colors orange, white and blue, arranged in horizontal bars of equal dimension, the orange being above, the white next and the blue below, with the following design in the centre, encircled with a laurel wreath greater in diameter than the width of the white stripe.
"Crest—Upon a hemisphere, an American eagle with wings displayed.
"Shield—The sun with shining rays rising from the sea.
"Legend—Upon a ribbon beneath the shield the words 'NE CEDE MALIS.'
"The said colors shall be the same as those of the flag of the Netherlands in use in the year 1639."
Section 2. This ordinance shall take effect immediately.
Which was referred to the Committee on General Welfare.
Alderman Brush moved that the Board do now adjourn.
The President put the question whether the Board would agree with said motion.
Which was decided in the affirmative...
P.J. SCULLY, City Clerk, and Clerk of the Board of Alderman.
Versions of the flag and seal exist with both stripes superimposed on the seal, or otherwise behind a white background. The official art, as illustrated in an annual report of the American Scenic and Historic Preservation Society contains a white background behind the seal, and an example of this can also be seen in this photo of the Bronx County Courthouse. Graphic standards do not exist for the official colors of the seal, and some City websites use Wikipedia's previous version of the seal as a reference, however several examples with a golden eagle, olive-green hemisphere, golden banner and yellow sun with orange rays on a white sky can be found from "Bronx Borough Day" pins from the early 20th century.
Own work, rendered from the original 1912 artwork
Simtropolitan