Travel American Airlines won’t fly 737 Max again until June at the earliest, even if it’s cleared sooner January 14, 2020 Dawn Gilbertson, USA TODAY Comments Off on American Airlines won’t fly 737 Max again until June at the earliest, even if it’s cleared sooner American Airlines says the move will result in the cancellation of 140 daily flights. Affected passengers will be rebooked or may get a refund.