I wish I had waited for your answer - I just signed up for KVS this AM. It sounds like I just wasted $ 30.
Here is the advice I got from Kiwi Flyer on AA forum:

You need to have signed up for Qantas frequent flyer. Then log in and search for awards (no need for miles in your account) online - make sure you pick classic and partner awards. The search engine shows all OW award availability (although there are ongoing issues with CX awards not showing properly).
Similarly for BA executive club. Sign up, log in and search for awards.

I will try this approach and whatever other suggestions I will get.
Good luck to us newbies!