If you want a cheap flight from Bangkok to Taipei, you've got zero airlines to choose from.
Taipei Taiwan Taoyuan International (Chiang Kai Shek International) Airport is just one of the airports in Taipei. If you're not set on a specific airport, try changing your search from Taipei Taiwan Taoyuan International (Chiang Kai Shek International) Airport to Taipei to see a broader range of flights – they might be cheaper.
If you're planning on going to Taipei during this time, you could take a look at other airport options. Or you could try to get a last-minute bargain.
