The flux in the transformer core can be assumed as the integral (over time) of the voltage at the inner winding, divided by the number of its turns. So that expression should work.

However, the currents will not work, since there is some loading applied to it.

The flux in the transformer core can be assumed as the integral (over time) of the voltage at the inner winding, divided by the number of its turns. So the expression for the voltage should taking only one of the windings.