I was there for a wedding around that time last year (Rarotonga) and can tell you that if I'd taken my gear I would have had 2 or 3 days in the week I was there that where kiteable, gear would have been on the larger end of my quiver as for the most part they would have been just kiteable. Having said this, where we were was less than ideal (Muri Lagon), sheltered so lots of flat water but due to islands on the outside of the lagoon (NE wind) wind was turbulent and a bit of shadow in places. if you are going to Aitutaki then I'd suggest this is more favourable as the islands are lower lying than Rarotonga.

In summary, if you can get away with it pack your gear and I'd be taking my bigger kite(s).