Burma Human Rights and Freedom Act of 2019 This bill authorizes aid to address the humanitarian crisis in Burma (Myanmar). It also calls for sanctions and reports related to the issue. Specifically, the bill authorizes aid for humanitarian assistance and reconciliation activities in Burma and other countries in the region, including assistance to help targeted ethnic minority groups and support voluntary resettlement. The President may not provide security assistance for Burma's armed forces until the Department of State certifies that the Burmese military has made significant progress in abiding by international human rights standards. The bill reinstates trade restrictions on rubies and jadeite from Burma until the President certifies that Burma has passed certain reforms relating to transparency in the gemstone industry. The President shall report to Congress a list of (1) senior military officials known to be directly and significantly involved in gross human rights violations in Burma, and (2) entities owned or controlled by such individuals. The State Department shall deny such individuals visas, and the Department of the Treasury shall impose various property-blocking sanctions against listed entities and individuals. The State Department shall report to Congress a strategy to promote economic development in Burma. The bill also requires reports on Burma's military, Burma's eligibility for preferential duty treatment, whether certain Burmese military officials should be on the list of specially designated nationals and blocked persons maintained by the Office of Foreign Assets Control, U.S. diplomatic efforts to impose coordinated sanctions related to Burma, and crimes against humanity in Burma.