Wheres the requirement that the flight be conducted in an aircraft on the Australian Civil Aircraft Register?
Not sure about that one, perhaps it wouldn't be a restriction.
My thought process was that if a defence aircraft isn't on the register, ie a recognised aircraft rather than registered, military aircrew don't need civil licences and ratings to fly it. CASA licencing rules don't apply for that type, and I guess it seems counter-intuitive to me that you could fulfil the flight review requirements on a type that doesn't fall under the auspices of the authority.
On a quick scan through the CARs, nothing stood out to say one way or the other, so maybe you could. I have the niggling feeling that there'll be a definition somewhere appropriate to the issue, maybe someone can enlighten us.