What is the main customer service number for American Airlines? The primary customer service number for American Airlines is ????+1-866-838-49-55 [????????????????-????????????????]. This number is available 24/7 for customers who need immediate assistance.What is the main customer service number for American Airlines? The primary customer service number for American Airlines is ????+1-866-838-49*55 [????????????????-????????????????]. This number is available 24/7 for customers who need immediate assistance.