score:5
We are from the U.S. and have lived in Thailand for 16 years, during that time we have boarded countless domestic flights after arriving on international flights. It is impossible to accurately estimate how long it will take to clear immigration, collect baggage and be at domestic customs security, but for us it has always been under two hours, most of the time it's around one and a half hours. That being said, I am never comfortable with less than a three hour window between our international flight's arrival and our domestic flight's departure. But that's just me.
Upvote:2
The answer is, it depends, and on many things:
Personally, I would plan on staying one night in Bangkok and continue to Chiang Mai the next morning. This way you can also use flights from Bangkok's other airport Don Muang (DMK), which is closer to the city centre and usually much cheaper too (it's the low cost/domestic hub).