E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Fly (plural flys).
A hackney coach, a cab. A contraction of Fly-by-night, as sedan chairs on wheels used to be called in the regency. These Fly-by-nights, patronised greatly by George, Prince of Wales, and his boon companions, during their wild night pranks at Brighton, were invented 1809 by John Butcher, a carpenter of Jew Street.
In the morning we took a fly, an English term for an exceedingly sluggish vehicle, and drove up to the Ministers.Hawthorne: Our Old House (Pilgrimage to Old Boston, p. 171).