The USSF is headquarted in the Pentagon, as are the United States' other armed forces.
The USSF becomes the sixth service of the U.S. Armed Forces, joining the United States Army, the United States Navy, the United States Marine Corps, the United States Coast Guard, and the United States Air Force.
The Air Force traces its roots through the United States Army Air Forces (6/20/1941-9/18/1947), the United States Army Air Corps (7/26/1926-6/20/1941), the United States Army Air Service (5/24/1918-7/26/1926), the Division of Military Aeronautics (5/20/1918-5/24/1918), the Aviation Section Signal Corps (7/18/1914-5/20/1918), the Aeronautical Division Signal Corps (8/1/1907-7/18/1914), and finally to its origin, the Aeronautical Division Signal Corps (8/1/1907-7/18/1914).
Before the Air Force, one has to go all the way back to almost the very constituting of the United States of America for the creation of the next youngest Armed Force, the Coast Guard, originally known as the The United States Revenue Cutter Service and the Revenue-Marine, created by Congress in 1790 at the urging of then-Secretary of the Treasury Alexander Hamilton to serve as an armed customs enforcement service.
The United States Marine Corps began life as the Continental Marines, created by the Second Continental Congress on November 10, 1775. It has been under the command of the Department of the Navy since the Congress' June 30, 1834, Act for the Better Organization of the Marines.
A month earlier, on October 13, 1775, the Second Continental Congress commissioned the Continental Navy, but it disbanded following the Revolutionary War. However, in direct response to Barbary pirate activity, the United States Navy was born with the Naval Act passed by Congress in 1794.
The Continental Army was created on June 14, 1775, by the Second Continental Congress, as America's first formal military service to fight during the Revolutionary War; it, too, eventually disbanded as hostilities with Britain calmed, only to be replaced with the implementation of the United States Army by the Congress of the Confederation on June 3, 1784.
* reddit user karanut published this idea for a USSF flag in 2018: