Battlefield Excellence through Superior Training Practices Act or the BEST Practices Act This bill requires the Department of Defense (DOD), no later than: (1) October 1, 2020, 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, 2022, to use only use human-based training methods for such purposes. The bill prohibits the use of animals in such training after the latter date, but permits DOD to exempt a particular command or training method from human-based training method requirements for up to one year if the human-based methods will not provide an educationally equivalent or superior substitute for live animal-based training methods. Allows exemption periods to be renewed. DOD shall submit an annual report to Congress regarding the development and implementation of the human-based training methods, including the justifications for any exemptions.