Clean Cooking Support Act This bill provides for a way of increasing the number of clean cookstoves and fuels for household, institutional, or commercial use throughout the world. The Department of State and the U.S. Agency for International Development (USAID) shall jointly establish the Clean Cooking Interagency Working Group to assist with overseeing the planning, management, and coordination of initiatives to increase the number of clean cookstoves and fuels worldwide. The State Department, USAID, the Department of Energy, the National Institutes of Health, the Centers for Disease Control and Prevention, and the Environmental Protection Agency shall work with the Clean Cooking Alliance to carry out clean cooking activities that relate to the missions of such departments or agencies.