There is a form on the CASA website for doing this in NZ due to the trans Tasman agreement. I'm not sure if there is another form for other OS countries.
As an aside, a flight review can be carried out by an instructor who does not have to be conducting it under a Part 141/142 school. CASA's attitude is that some training would normally occur so therefore the FR would be conducted by a school, but it's not a legal requirement.
I'm not sure what rego you would write on the form....
As has been said, the whole intent of introducing Part 61 is to be ICAO compliant, so any ICAO instructor should be able to carry out this role.