Measure leakage inductance of flyback transformer with multiple secondary windings
what is the best method to measure?



Short the primary and test each secondary separately. The measured inductance (for each of the three tests) is the leakage inductance referred to the secondary. 
You could short each secondary and measure inductance at the primary but then you'd need to divide by the turns ratio squared to be able to place it in a model on the secondary side.


It all depends on what you are trying to achieve.

Regards actual measuring devices, you could use a meter that measures current and do some calculations to determine impedance and remove any DC resistance artefacts from the answers leaving you with inductance. Or, you could use an LCR meter operating at a frequency that is appropriate for the transformer type.