HKG-BKK is definitely 18. JFK-HKG I think is probably 18 as well, but I am not 100% sure about this. I would suspect that once the aircraft is in the air, it follows the laws of its country of registration and for CX that means Hong Kong law.
I think possibly the only exceptions to this rule are on "domestic" flights operated by CX within US/Canada. For example, if you're flying from YVR-JFK on CX, then I don't know what the rules might be and maybe it's 21 (as you already "enter" the US in YVR itself).
However, really, whatever the official rules may say, if you look 18 they probably won't make a fuss about it (unless you do). Crew are trained to ensure that those who are intoxicated don't get any more alcohol.
I bet that cxcabincrew has a definitive answer to this, if he/she is reading this thread.