Most regiments in the Revolutionary War (both American and Crown Forces) had flags, called colors or flags, serving not only as identification for where a unit was on the battlefield they were held in high regards by the men serving in the regiments and their keep was a point of pride for soldiers.
This is a photograph of the 2d Dragoon's Flag known as the National Flag. National Flags are quite often striped and Regimental and Troop flags are usually solid in color. This flag was taken at Pound Ridge in 1778 by Banastre Tarleton and kept by his family until 2005. The flag sold at auction by Sotheby's for $12.7 million dollars on Flag day, 2007
Photo of Original Regimental Flag from 1904 copy of Tallmadge's Memoirs
Photo of Original Troop Flag Currently on display at the Smithsonian (The flag has faded from red)