Hinckley was born in Craighwell, a hamlet of Boston, to a poor family that originated in Britain. Josh Hinckley worked as a bartender at a tavern, The Flashy Falcons Pub. When the Revolutionary War began, he purchased a musket for $50 and raised a militia in the town of Craighwell, mustering 120 young males, many without any experience with the military. However, Hinckley had seen some action in Dunmore's War, serving in the army in 1774. The militia won at Cavern Hill, with Hinckley becoming a Colonel in the Militia. However, his force was decimated at Caldwell, where a Scottish Guard of 150 troops devastated his army.
During the skirmish, Hinckley was at the front of his troops, sword in hand, and he directed them into battle. However, he was not at the front for long, for his leg was broken by a musketball, shattering his bone. He was pulled to the medical center, an impromptu main camp, and the medician did not have any supplies. Reportedly, the last words of Hinckley's were: "You (Doctor) don't have any medicine left? Then what does that make you now? " He passed away afterwards, and the medician allegedly took up a musket and shot Private First-Class Connor Weatherly, before being gunned down.