The best most of us could do is look up those flights using expertflyer (EF) and that's a huge list. If you're really looking for success in these bookings, I'd recommend you head on over to
expertflyer.com, create an account for as little as $4.99 a month for 250 queries and you can query the flights yourself and track as you get closer to departure.
As an example, here's ticket availability for CX846 HKG-JFK on MAR 22 2020 - F5 A5 Z0 J9 C9 D9 I9 U W9 R9 E9 T4 Y9 B9 H9 K9 M9 L9 V9 S9 N9 Q9 O9
The coding here is fare class code followed by number of tickets available with a max of 9. First class fare codes are F,A,Z. Business class J,C,D,I. Premium economy - W,R,E and the rest are economy.
First class award is fare class Z and this flight is currently showing no award (redemption) available. Unfortunately, for biz class there is no award class shown on EF. The best indicator is discounted business class, I. And this flight is showing at least 9 I class seats available - I9. In fact, all the flights from HKG - JFK/EWR are showing I9 on that date. A quick check of BKK-HKG flights on the same date shows a similar picture, biz class availability wide open, i.e. J9 C9 D9 I9
This is typical, as MAR 22 isn't a special day that I know of and being more than 3 months out, the flight is wide open. So why would a redemption not be available? Same reason as most of the other responses in this thread, it's too far out and CX hasn't released any award space. They're holding their cards, and looking to make revenue and awards get released closer to departure when the picture becomes clearer.
So if you're really determined to get an award on that date, the best approach is to waitlist the flight that makes the most sense for you, pay for EF and monitor the situation yourself. As you get closer to departure date, and if ticket availability on EF starts to narrow, make a decision about what you want to do which might involve choosing a different flight or if you really need to travel then buying a ticket outright. Don't be surprised that waitlist may expire and then it's a free for all, which involves checking daily right up until departure. As departure date closes in and there are unsold tickets, CX starts freeing up some award space. That's been the situation for a while now. You could also luck out and have award space open earlier and your waitlist is confirmed. Either way it's a crap shoot and if you've read this thread you can see how frustrating it has been for many to redeem awards.
For J (biz) class from HKG-NYC, I'd generally advise against CX899. The A350 has less J seats available and the flight tends to fill up, even on Sundays which I usually travel on CX899 when I return back to NY on an upgrade redemption. CX846 is slightly better chance as it's got more J seats, has F (first) if you want to try for that and it's the second afternoon flight after CX840 which is typically more crowded. Not too sure about CX888 since I never take that flight, but the stop in YVR makes it less desirable,