How to Calculate Saturation Current of a Transformer?
There are two types of transformer

1) High (ideally infinite) permeability, used as power transformers
2) Low permeability, used as flyback transformers, where \$I_{sat}\$ is a key specification

The difference is that a power transformer is not intended to store energy in the core, that's minimised in the design. While it does have a net current that will saturate it, that current is very small compared to the load current, and we don't control that current directly, as it's the algebraic total current flowing in all the windings. This total current is called the magnetising current. The load current by itself is irrelevant.

In a power transformer, we control the magnetising current by controlling the voltage and time of the input waveform. Each core has a \$Vs\$, a volt.second product, that it can support before core saturation. Increase the input frequency, and you can increase the voltage. 

You can calculate the Vs product from the cross section of the core, and knowledge of the maximum field before saturation. Vs = flux (Webers) = core area (m2) * field (Tesla).

In a power transformer, you usually swing from -ve flux to +ve flux, so would use 2x the maximum field. In a pulse transformer, you may be gong from zero field to max, so would only use 1x maximum field. Take care to reset the flux back to zero before the next pulse of the same polarity.