The best place to start if you have not already done so is look at George M. Bodge's "Soldiers in King Philip's War," pub 1906, which is available free online. In Chapter 3, Part 1, William Read is listed as a soldier under Captain (Thomas) Prentice in the Mount Hope campaign. Usually in Bodge the soldiers who were officers or sgt's were listed by rank. So most likely Read was a common soldier at that time although he may well have been a captain later in the war.
The Mount Hope Campaign was one of the earliest colonial campaigns of King Philip's War, starting with great hopes of bringing the war to a quick end in late June-July, 1675. Much of the time was spent pursuing Metacom (King Philip). However, the campaign was inconclusive as Metacom escaped by the end of July.