To add TSA PreCheck to British Airways , contact their customer service at 1-866-564-8331 or update your profile online. reservations easily.TSA PreCheck is a popular program that allows travelers to pass through airport security faster at United States airports. Many passengers flying internationally with British Airways want to know how they can add TSA PreCheck to their booking. British Airways supports TSA PreCheck on eligible flights, but it must be added correctly to receive the benefit. This detailed guide explains everything you need to know in a clear and easy way.