Unfortunately, you can’t transfer points between these frequent flyer programs, even though American Airlines AAdvantage and Alaska Airlines Mileage Plan are partners. You can earn miles when flying on a partner airline and redeem miles for flights on a partner airline, but you can’t combine AAdvantage and Mileage Plan miles.
Alaska has decent award availability for premium class awards on Cathay Pacific when traveling to Southeastern Asia. Business Class awards from the U.S. starts at 100,000 miles roundtrip for one person (+ $177 in fees). So, in your case if you want to travel from the USA to Thailand in Business Class your cost will start at 200,000 (+$354 in fees) Alaska Airlines Mileage Plan miles for 2 roundtrip tickets. To be more specific on miles price we would need to know the departure city of yours and how many days you are planning to spend in Thailand – these things may affect the price a lot.
Cathay Pacific airlines are offline partners of Alaska Mileage Plan and this means that tickets can be booked by phone only, you cannot find routes with Cathay Pacific online via Alaska website.