Wildfire Smoke Relief Act This bill provides for assistance for the purchase of smoke inhalation prevention equipment to specified individuals at risk of wildfire smoke-related illness. The President, in carrying out the Transitional Sheltering Assistance Program of the Federal Emergency Management Agency (FEMA), shall provide (1) assistance to a state or local government, local public health authority, or a coordinated care organization to purchase and provide such equipment to at-risk individuals; and (2) cost-efficient transitional shelter assistance to at-risk individuals in any case in which such equipment is insufficient to mitigate the risk of illness.