Prevention of Arms Race Act of 2019 This bill restricts the appropriation of funds for the procurement, flight testing, or deployment of missiles banned by the Treaty between the United States of America and the Union of Soviet Socialist Republics on the Elimination of Their Intermediate-Range and Shorter-Range Missiles (INF Treaty). Before such funds may be appropriated, the Department of Defense shall submit a report to Congress that includes (1) a memorandum of understanding from a North Atlantic Treaty Organization or Indo-Pacific ally committing to hosting the deployment of such a missile, (2) confirmation that the United States has not rejected any diplomatic offer to resolve Russia's violation of the INF Treaty, (3) discussion of the ramifications of a collapse of the treaty and of a U.S. withdrawal from the agreement, (4) discussion of the mission requirements with respect to Russia and China that would be met by weapons systems covered by the INF, and (5) discussion of the degree to which INF-compliant weapons can meet such mission requirements.