Measuring Transformer Magnetizing Inductance
The easiest way is to connect the open-circuited transformer and observe the current circulating in the primary side. The frequency is adjusted so that the current remains discontinuous over a switching period. The demagnetization time is quite long as it is given by the off-slope \$V_f/L_p\$ therefore the switching frequency will probably be a few hundred of Hz.

The generator will drive the MOSFET on and off with a square-wave signal featuring a peak value of 10-12 V to ensure the right turn-on sequence. When you apply the dc voltage across the inductance by turning the MOSFET on, the current starts from 0 (the current is discontinuous with a low frequency) and grows to a peak value with a slope equal to \$\approx\frac{V{_{in}}}{L_p}\$ where \$L_p\$ is the inductance you want. If you observe the current across the \$1-\Omega\$ resistance, you should see something like below:


You select a portion of the current and measure \$\Delta t\$ and \$\Delta I\$. You compute the slope by \$S=\frac{\Delta I}{\Delta t}\$. This slope is equal to \$S=\frac{V{_{in}}}{L_p}\$. You can now extract the inductance value following \$L=\frac{V_{in}}{S}\$. Assume you measure a slope equal to 10 kA/s (10 V applied across a 1-mH inductance) and the source is biased to 10 V. Then the inductance is \$L=10/10000=1\;mH\$. You have to know that depending on the transformer model, the measurement may include the leakage inductance term \$l_l\$. In this case, the measured slope is \$S=\frac{V{_{in}}}{L_p+l_l}\$.

With this circuit, you can now either increase the source voltage or the on-time (keep the current discontinuous) and check the saturation current \$I_{sat}\$ as shown below. The best is to do this experiment when the core is at its highest operating temperature.