From the
Antique Bottle & Glass Collector Magazine:
"On this side of the Atlantic, the Liberty Cap, or what we called the French Liberty Cap, became a well-known symbol. During and after the French Revolution, the Liberty Cap, represented as being held aloft on the end of a pole, symbolized not only freedom, but also the fight for that freedom. In the flask arena, GI-85, GI-86, and GI-87 have the Liberty Cap, on the end of a pole, on one side. The other side (and it should come as no surprise to anyone) contains a bust of a man, surmounted by the word "Lafayette".
But to the common man, probably the representation of Columbia (or Liberty) that was encountered most often was that which appeared on our currency from 1793 until the 1830s.
The version of Liberty used on the half-dime (1829 – 1837), dime (1809 – 1837), quarter (1815 – 1838), half dollar (1807 – 1839), quarter eagle (1808 – 1834), and half eagle (1807 – 1834), is very similar to the representation of Liberty that is on a majority of the historical flasks. It’s certainly quite likely that the images from the coins served as a model for the mold makers. The mold makers, realizing the popularity of the Liberty image, capitalized on this by making flasks that copied this idea. I follows then, that these flasks were made after 1807, and probably before 1840, when Liberty was highly modified on the United States coinage.