Veteran Prescription Continuity Act This bill amends the National Defense Authorization Act for Fiscal Year 2016 to direct the Department of Veterans Affairs (VA) to furnish an individual who is transitioning from Department of Defense (DOD)- to VA-furnished medical treatment any pharmaceutical agent not included in the joint uniform formulary if a DOD health care provider determines that the pharmaceutical agent is critical for the transition. The VA shall furnish an individual with such pharmaceutical agent: (1) beginning when the individual enrolls in the VA health care system, and (2) ending when a DOD health care provider determines that the individual does not require the pharmaceutical agent.