Burma Human Rights and Democracy Act of 2014 - Prohibits FY2014 or FY2015 funds from being made available for security assistance to the government of Burma unless the Secretary of State certifies to Congress that: (1) Burma has taken steps toward establishing civilian oversight of the armed forces, addressing human rights abuses by the military, and terminating military relations with North Korea; (2) Burma has taken steps to establish a fair and inclusive process to amend the Constitution of Burma, including the full participation of the political opposition and ethnic minority groups; (3) Burma has amended its constitution and laws to ensure civilian control of the military; (4) Burma is promoting peace agreements or political reconciliation and is addressing the resettlement and humanitarian situation of displaced persons; and (5) the Burmese military is improving its human rights record, taking steps to withdraw forces from conflict zones, and implementing a code of conduct.

States that nothing in this Act should be construed to prevent participation by Burmese authorities in training on civil-military relations and human rights, as carried out by the Defense Institute of International Legal Studies, or to prevent U.S. disaster assistance in Burma.

Directs the Secretary of State to report annually to Congress on the status of military-to-military engagement between the U.S. Armed Forces and the Burmese military.