Acupuncture for Our Heroes Act of 2019 This bill requires the Department of Veterans Affairs (VA) to provide qualified acupuncturist services to veterans enrolled in the VA health care system. A qualified acupuncturist is an individual who is licensed, certified, or otherwise accredited and may be appointed as an employee of the VA or as a contractor. The VA shall carry out such program in at least one VA facility in each Veterans Integrated Service Network (regional VA health care administrative areas) in both urban and rural areas. The bill requires the VA to establish the Advisory Committee on Acupuncturist Services, which must advise the VA on governing protocols and review and evaluate the ability of a veteran to access an acupuncturist at VA facilities.