| Nonstop Flights: Austin to New Orleans $138 r/t [August-September] â American Airlines American Airlines has round-trip flights from Austin (AUS) to New Orleans (MSY) for $138, NONSTOP. Flights are mostly August to September. Tuesdays, Wednesdays, and Saturdays. Extended weekends available. A Carry-on bag and also a personal item is allowed for free on American. Click for more details and booking links Nonstop Flights: Austin to New Orleans $138 r/t [August-September] â American Airlines . | 