The Alaska Airlines card is issued by Bank of America, so you'll need to contact your bank's customer service. There are 3 ways to do this:
Call Bank of America Credit Card Customer Service at (800) 732-9194 to speak to a customer service agent. And let the representative know that you intend to cancel your Alaska Airlines credit card.
Visit your local financial center to speak with a personal banker
Send your request in writing to:
Bank of America
P.O. Box 982234
El Paso, TX 79998-2234