To seek compensation for a delayed American Airlines flight, familiarize yourself with the American Airlines Flight Compensation Policy. Ensure you meet eligibility criteria, such as the delay exceeding a specified duration. Keep documentation of the delay, including flight details and any expenses incurred. Submit a claim through the airline's official channels, providing necessary information and supporting documents. Promptly follow up on your claim and stay informed about the status. Airlines typically offer compensation in the form of vouchers or travel credits.