The New York City firm of Annin and Company (or Annin Flagmakers) began at Fulton and William Streets in Manhattan in 1847, Its address was nicknamed “Old Glory Corner” because it made so many U.S. flags (called “Old Glory”). In the 1910, the company moved to 85 Fifth Avenue (at 16th Street), and this new address became “Old Glory Corner.”
 
Annin Flagmakers moved to New Jersey and the “Old Glory Corner” name is now historical.
 
   
Wikipedia: Old Glory
Old Glory is a nickname for the flag of the United States. The original “Old Glory” was a flag owned by the 19th-century American sea captain William Driver (March 17, 1803–March 3, 1886), who flew the flag during his career at sea and later brought it to Nashville, Tennessee, where he settled. Driver greatly prized the flag and ensured its safety from the Confederates, who attempted to seize the flag during the American Civil War.
 
Annin Flagmakers
About Annin - History
The American flag was scarcely 70 years old in 1847 when brothers Benjamin and Edward Annin founded Annin Flagmakers flag–makers on Fulton Street in New York City. The business had begun with their father, Alexander Annin who had been sewing flags and supplying them to merchant ships from his sail-making shop on the New York City waterfront as far back as 1820. There, the company prospered and grew along with our nation.
 
In 1865 Annin Flagmakers experienced its first big surge in business when the Civil War ignited the fires of patriotism in the American populace. This was the first time in America’s history that private citizens purchased American flags in significant numbers to display on their homes.
 
In 1910 Annin Flagmakers relocated to 5th Avenue and 16th Street, a location that later came to be known as ‘Old Glory Corner’. Increased demand for American flags coincided with our country’s industrial revolution in the latter part of the 19th century. Annin Flagmakers, on the forefront of technology, then as it is today, made the sewing machine, invented in 1846, a standard piece of flag-making equipment.
 
Chronicling America
11 December 1914, The Arizona Republican (Phoenix, AZ), “Berryhill’s 1914-1915 Arizona Mail Order Catalog,” pg. 6, col. 1 ad:
Our fine line of Flags, Buntings and Decorations is made by the leading flag makers in the United States, the 70-year-old firm of Annin and Co., “Old Glory Corner,” New York City.
(The Berryhill Co.—ed.)
 
Google Books
May 1917, The Edision Monthly, “After Betsy Ross,” pg. 441:
... all these (flags—ed.) and many others were made in the four-story red brick building a William and Fulton streets which houses the establishment of Annin and Company. It is this establishment and the industry it houses which long ago created the name “Old Glory Corner.”
 
12 July 1950, New York (NY) Times, “UN Battle Flags Ready for Korea,” pg. 8, col. 2:
The order went to Annin & Co., at 85 Fifth Avenue, largest flag manufactory in the world and oldest in this country, over the weekend. The experienced seamstresses in the company’s workshop on the second floor of “Old Glory Corner,” as the building at Fifth Avenue and Sixteenth Street is called, began work on Monday.
   
Google Books
Bonds of Affection:
Americans Define Their Patriotism
By John E. Bodnar
Princeton, NJ: Princeton University Press
1996
Pg. 76:
The Annin Company, founded in 1847 and the first large-scale flag manufacturer, advertised its firm as “Old Glory Corner” with a front-page photo of its factory flying American flags from all four stories.
     
Asbury Park (NJ) Press
Annin flagmakers in business since 1820
BY DOCENTS OF THE NJ MARITIME MUSEUM, 3:48 p.m. EST November 25, 2016
(...)
Annin Flagmakers started as a ship chandler in New York in 1820. Alexander Annin sold items of the time: whale oil, oakum, varnish, twine, turpentine, and everything for sailing ships. In addition, he made sails for sailing ships. He was soon joined by his sons Benjamin and Edward who started making flags of all types at their waterfront store. For years they were located in Lower Manhattan in a location nicknamed Old Glory Corner.
(...)
Today the Annin corporate headquarters are in Roseland, NJ. They have purchased other companies and manufacture at a few other locations. Flags are sold to retailers. They employ over 500 people.