Global Fragility Act of 2019 This bill directs the Department of State to establish the interagency Global Fragility Initiative to stabilize conflict-affected areas and prevent violence globally, and establishes funds to support such efforts. The State Department shall devise a plan for the initiative, including its organizational structure and goals. The State Department shall lead in foreign policy, diplomatic, and political efforts. The U.S. Agency for International Development shall lead in development, humanitarian, and non-security policies. Other departments and agencies, including the Department of Defense, shall provide support as necessary. The State Department shall select priority countries and regions that are particularly at risk, and report to Congress 10-year plans for each. Each plan shall include information including descriptions of goals, plans for reaching such goals, and benchmarks for measuring progress. The State Department shall report to Congress every two years about the initiative's progress. The Government Accountability Office shall consult Congress every two years about opportunities to assess the initiative and recommend improvements. The bill creates the Stabilization and Prevention Fund to support efforts to stabilize conflict-affected areas, including areas at risk from the Islamic State of Iraq and Syria or other terrorist organizations. The bill establishes the Complex Crises Fund to support programs to address emerging, unforeseen, or complex challenges abroad.