Thai Airways flies to Chiang Mai from both Don Muang and Suvarnabhumi.
You can tell which airport to go to based on the flight number:
Thai Airways flights at Don Muang airport have a four-digit number code beginning with 1, such as TG1203.
Flights at Suvarnabhumi airport use three-digit numbers, such as TG203
The full domestic schedule from both airports is posted on the Don Muang site:
http://www.donmuangairportonline.com/thai-airways
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