United States Technical Assistance for Mexican Labor Capacity Building Act of 2019 This bill requires an increase in the amounts transferred to the Trade Enforcement Trust Fund and the use of such amounts to implement labor obligations in the free trade agreement with Mexico. Specifically, for the implementation and monitoring of labor obligations in the free trade agreement with Mexico, the bill designates certain funds be provided (1) to the Office of Trade and Labor Affairs at the Department of Labor; (2) to the Office of Child Labor, Forced Labor, and Human Trafficking at Labor; and (3) for three permanent Labor Attachés at the U.S. Embassy in Mexico or consulates of the United States in Mexico. For international development, the bill designates certain amounts to be transferred to the U.S. Agency for International Development to monitor trade agreement obligations related to anti-corruption and the promotion of rule of law.