Battlefield Excellence through Superior Training Practices Act or the BEST Practices Act - Requires the Secretary of Defense (DOD), no later than: (1) October 1, 2016, to develop, test, and validate human-based training methods for training members of the Armed Forces in the treatment of combat trauma injuries, with the goal of replacing live animal-based training methods; and (2) October 1, 2018, to use only use human-based training methods for such purposes. Prohibits the use of animals in such training after the latter date. Provides an exception when the Secretary determines that human-based training methods will not provide an educationally equivalent or superior substitute for live animal-based training methods. Requires an annual report from the Secretary to the congressional defense committees on the development and implementation of the human-based training methods, as well as any exceptions implemented.