If you file the chargeback for a cancelled flight 90%+ they won't dispute it, don't waste your time with all this DOT stuff and trying to handle things nicely. If you file chargeback most likely the credit card company won't even ask for all this proof other posters here are asking saying they will unless there airline chooses to dispute, they'll just give you a temporary credit, and then if they don't hear back from the airline, which they probably won't, you'll get the full credit.
Just file the chargeback and move on is the smartest move.