[C210N]

DC already has a flag. It has a star already representing DC.

Note this flag has 3 stars. One for City of London, one for the Vatican, and one for DC.

[NorthMountain]

Here's a real history of the Washington DC flag. It's derived from George Washington's family coat of arms.

[Catholic and Conservative]

According to Charles A.R. Dunn, who designed the flag of Washington, DC, the flag is based on the coat of arms of George Washington, which had three stars.

https://skeptics.stackexchange.com/questions/14007/do-the-3-red-stars-on-washington-dcs-flag-represent-3-city-states#answer-14009