Back to the OP, it is a great pity that RAFAT can't make it out to NZ, given that there is the 80th Anniversary of the founding of the RNZAF in 2017, but the practicalities are sadly clear. For anyone mildly interested in history of the RAF, it is instructive to see the involvement of early RAF aviators such as Salmond and Cochrane in shaping the RNZAF.
Nice sentiment, but it won't fly [sic]. The RAF couldn't make it to the RNZAF 75th Anniversary in 2012, so highly unlikely to give any consideration to the Reds! [Personally I would prefer a Typhoon display team anyway!]
Besides, the UK having discarded Australia and New Zealand in 1973 in favour of the EU, there simply isn't the will to do it.