Allied Burden Sharing Report Act of 2019 This bill directs the Department of Defense to report to Congress on (1) the defense spending and military activities of certain countries with cooperative defense agreements with the United States, (2) whether a country places limits on the use of funds contributed to the common defense, and (3) any U.S. actions to minimize such limitations. The report shall cover each North Atlantic Treaty Organization (NATO) member state, each Gulf Cooperation Council member state, each country party to the Inter-American Treaty of Reciprocal Assistance (Rio Treaty), and other specified countries.