Many members of the Watson family and the Darnell family lived in the area, and I have no doubt that Twain meant to describe a feud between families of those names. However, he garbled the details badly. Although the area was very violent, the routine bloody ambushes Twain suggests between Darnells and Watsons don't seem to have actually occurred. During this time, a Darnell daughter was married to Robert Watson, son of the Watson patriarch, Daniel Watson.
There was a shooting in 1859 between a Mr. Beckham (married to a Watson), a Mr. Starr (a friend of Beckham), and a Mr. Shultz (apparently also related by marriage to the Watsons). Twain claims to have nearly been present for this shooting, which was widely reported in newspapers of the day, but not described as a feud, and no Darnells seem to have been present.
In 1863, Beckham, his father, and four of his children were murdered by Union soldiers (also widely reported at the time). No Darnell was involved.
A later ambush murder in 1869 involved the deaths of a man named Edwards and two men named Lane (one of whom was supposedly related by marriage to the Darnells). Twain reports this as the murder of the last Darnells by a group of Watsons. In fact, the shooters were three Darnells, who survived unscathed.