VA Precision Medicine Act This bill requires the Department of Veterans Affairs (VA) to implement the Precision Medicine for Veterans Initiative to identify and validate brain and mental health biomarkers among veterans, with specific consideration for depression, anxiety, post-traumatic stress disorder, bipolar disorder, and traumatic brain injury. The VA must develop data privacy and security measures to ensure the information of veterans participating in the initiative is kept private and secure. Additionally, the VA must make de-identified data collected under the initiative available for research purposes both within and outside of the VA. Data collected under the initiative may not be sold. The VA must also assess the feasibility and advisability of coordinating efforts of the initiative with the Million Veterans Program.