Veterans Health Care Trust Fund Act This bill requires the Department of Veterans Affairs (VA), upon the commencement of any war, to establish a trust fund to be named for that war. Amounts collected pursuant to a war tax (required by this bill) shall be deposited into such fund and may be used by the VA to provide for veterans who serve on active duty during that war programs and benefits directly related to their health care. For any fiscal year during which the VA makes a withdrawal from such a fund, the Government Accountability Office shall conduct an audit of the consolidated financial statements relating to the fund. The bill amends the Internal Revenue Code to provide for the imposition upon individuals who have not served on active duty in the Armed Forces of a graduated income tax with respect to each war occurring at any time during the taxable year.