The District of Columbia is a separate nation it is incorporated under the British crown in Puerto Rico under THE UNITED STATES OF AMERICA inc. It has its own constitution, its own flag and its own laws separate from the United States of America.
the Capital of THE UNITED STATES OF AMERICA is Washington DC in the district of Columbia. The capital of the United States of America is Philadelphia.
the UNITED STATES OF AMERICA's flag is a yellow fringe around the United States flag, this yellow fringe represents the flag has been captured, an Eagle ontop of the flag represents captured flag, there should be no symbol on top of the flag.