The fictional date
If Quincannon, Frontier Scout was about real history, it might be easy to figure out when it happens.
Some of the action happens at Fort C.F. Smith, Montana. Fort C. F. Smith was occupied by the US army from 1866 to 1868, when it was abandoned and burned by the Sioux. So in real history the film would have to happen in 1866 to 1868.
Quincannon was once a captain in the 7th US cavalry but resigned after the Sand Creek Massacre, which was on November, 1864. (but the 7th US cavalry wasn't formed until 1866). Quincannon also mentions the Washita battle or massacre on December 27, 1868 as a past event, which doesn't make sense since no snow is ever seen on the ground.
Of course, the possible dates of events in the movie could be very different than in real life.
It is rather amusing that characters worry that if the Sioux, Cheyenne, and Arapaho get 800 Henry repeating rifles they will be able to close the Bozeman Trail to white travelers.
In real history the Sioux and allies didn't manage to steal 800 Henry repeating rifles, but they did manage to steal so many horses and murder so many travelers on the Bozeman Trail that almost nobody dared to use it after 1866, instead choosing the safer Bridger Trail to reach the gold region in western Montana.