Keeping Our Promise to America's Military Veterans Act - Expresses the sense of Congress that, in order to express the gratitude of the American people for the sacrifices of America's veterans and their families, legislation should be enacted that: (1) assures timely and adequate funding of the Department of Veterans Affairs (VA), especially for medical care activities; (2) improves the ability of the VA's Veterans Benefits Administration to provide timely and accurate decisions on claims for veterans benefits; (3) assures that the VA provides timely access to high-quality treatment for mental health conditions; and (4) facilitates a seamless transition from military to civilian life for members separating from the Armed Forces and their families.