Taipei City Taiwan Taoyuan Intl airport offers the cheapest routes to Bangkok, from ฿5,407; whereas Kaohsiung City airport is typically cheaper if you're flying to Bangkok, from ฿10,377. It's best to make sure you are flexible on dates to find the cheapest possible flight options for your journey.
Here are some of the cheapest flight destinations from Taiwan:
Fly from Taipei City to Bangkok from ฿5,407
Fly from Taipei City to Chiang Mai from ฿6,615