Among his best known designs are the obverse (front) and reverse of the United States quarter dollar featuring the profile of George Washington, a coin that has been in continuous circulation with some modifications since 1932.

He designed both sides of the quarter, adapting the obverse profile of the United States's first president from a bust of Washington initially produced by French neoclassical sculptor Jean-Antoine Houdon in 1786.

In 2021, after the "America the Beautiful" coin series ended, Flanagan's design for the obverse of the quarter returned for one year, with the reverse changed to Benjamin Sowards' engraving of Washington crossing the Delaware.

The inscription on it reads, 'They Shall Not Pass', and the medal is found in the Lafayette Database of American Art in French National collections.

From 1885 to 1890, Flanagan was a studio assistant to Augustus St. Gaudens and worked on several large projects.