AA didn't charge you $19.
You ask for a refund from the company you paid for the service.
Your credit card provider should have contact information for the company you paid. Additionally, you should have gotten a receipt via email when you made the purchase.
I see no reason a chargeback would be needed here. The companies providing internet service for domestic and international flights are reputable companies who understand service to jets flying 500 knots at 40K feet isn't always going to work.