Vaccines for Veterans Act This bill authorizes the Department of Veterans Affairs (VA) to furnish the COVID-19 (i.e., coronavirus disease 2019) vaccine during the COVID-19 emergency period to veterans who were discharged from service under honorable conditions, regardless of whether they are enrolled in the VA health care system or are otherwise eligible to receive VA health care. Under the bill, the directors of VA medical facilities are authorized to determine priorities among eligible veterans to receive vaccines in accordance with state guidelines. The VA must coordinate with various entities (e.g., the Department of Defense) to determine whether an individual seeking to receive a vaccine meets the requirements set forth in this bill and the relevant prioritization for such individual.