The Inspector wrote:
I believe the CORSAIR in question is wearing NZAF markings which were a big blue/white/yellow roundel with big blue flanked white bars so the markings 'looked' like U.S. so they didn't get bagged by friendlies, maybe Mr. Cook has some pix of F4U's in NZAF or ANZAC markings

That Corsair is a US aircraft. I have seen better quality footage of - I believe - the same clip. The RNZAF very seldom had opportunity to operate its Kittyhawks and Corsairs in the same airspace operationally and these P-40's are wearing operational markings. RNZAF P-40's and Corsairs did indeed fly together at home in NZ from stations such as RNZAF Station Ardmore. But I am coinvinced this is a US Marine or US Navy Corsair.
The RNZAF P-40's operated regularly with US aircraft on strikes, flying as escorts to US bombers (medium and heavy, and dive bombers) and often US escorts were along with them.
As for the quote above, the statement "big blue/white/yellow" is incorrect. The roundels began as standard RAF type with red centre, white, blue and yellow outer. The red centre was removed because of too many incidents when US fighter pilots attempted to, some succeeding, shoot down their RNZAF Allies due to poor markings recognition. The red was painted blue to reduce mistaking it for a red Japanese roundel. Later after this film was taken the blue centre of the roundel was reduced to just 3 inches to even more make the RNZAF aircraft recognisable as allies.
The yellow outer roundel colour of the markings only appeared on some aircraft and this was because our markings were painted over factory applied RAF and USAAF markings and so the outer colour was retained in some cases. It's a very complicated business and I recommend Warren Russell's books on RNZAF and NZPAF markings for further reading to understand all the variatuions.
As for the other usage above of the term NZAF - the New Zealand Air Force never had its own aircraft and disolved long before the war becoming the New Zealand Territorial Air Force. These aircraft belong however to the RNZAF, the regular service that before June 1934 was referred to as the New Zealand Permanent Air Force.