After finding the airline surprisingly resistant to his damaged bag claim, Lee turned to Consumer Rescue. American Airlines tags this bag as priority at LAXLee routinely flies between Los Angeles (LAX) and New York City (JFK). The $1,700 bag was reduced to a pile of crumpled aluminum while in the care of American Airlines. He used those receipts to back up his eventual damaged bag and missing items claim with American Airlines. How to file your American Airlines damaged luggage claimAmerican Airlines makes filing a damaged or missing luggage report very easy.