The authorization for a special federal district, not to be a part of any state, as the seat of national government was laid out in Article I, Section 8 of the Constitution, which grants the Congress authority
To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings;
Conveniently, the Constitution now spends most of its time in "such District." Now, I once thought that the creation of the Federal District was mandated by the Constitution, but the excerpt above suggests that Congress was allowed, but not required, to establish a seat of federal government distinct from any state. Anyway, the Federal District was established along the Potomac River, on land ceded from Maryland and Virginia - though Virginia got its cession back in 1846. Until then, the District of Columbia had been divided into two counties: the county of Washington on the north bank, and the county of Arlington on the south. Similarly, there were multiple municipalities in the District: until 1871, letters could be properly addressed to Georgetown, DC. The Organic Act of 1871 unified the City of Georgetown, the City of Washington, and the County of Washington into a single legal entity, the District of Columbia.
So, while DC as we know it came into existence in 1871, it wasn't until 1938 that it adopted its spiffy red-and-white flag. The banner is based on the three stars and stripes from the shield on George Washington's family coat of arms. I heartily approve - it is instantly recognizable, and simple enough for schoolchildren to draw. The citizens of the Federal City seem to dig it - it appears on non-governmental logos and is flown from non-governmental buildings throughout the District.
The official motto of the District - Justitia omnibus ("Justice for all") - and the license plate slogan, "Taxation Without Representation," are not-so-subtle digs at the governance of the Federal City. Citizens of DC have a non-voting delegate in the House of Representatives, and only won the right to vote in presidential elections in 1961, with the ratification of the 23rd Amendment to the Constitution (they didn't actually get to vote until the presidential election in 1964).
As far as I can tell, the selection of the wood thrush (Hylocichla mustelina) as the official bird, or the scarlet oak as the official tree, of the District carries no specific political message. Too bad.