Back EMF in a transformer with an external power source to the secondary coil
and the secondary current so produced creates a flux equal and
  opposite to that produced by the primary winding


I think there may be some misconception here. The secondary current that flows is because of the load on the secondary. This produces a flux that is entirely cancelled by the increase in primary created flux caused by that load.

In other words there is still the magnetization flux due to magnetization current. That magnetization current always flows irrespective of load or secondary currents.

Now, if the transformer was driven backwards and you observed the voltage rating on the secondary, the flux produced by those fewer turns would be the same as when it was originally energised the “intended” way.

A slightly more accurate result of the transformer being driven backwards is that the magnetization flux would be a tad less. This is because the turns ratio might be tailored to the “right” output voltage under load conditions and, due to transformer regulation issues, the secondary turns might be a tad higher. This would result in higher inductance and less magnetization current when driven backwards.

If both primary and secondary are driven in the right polarity i.e. observing the correct phase relationship between primary and secondary AND, they are driven with voltages that match the relative turns on each winding, then each winding will contribute 50 % to the magnetization flux. 

If either of those “ifs” are not adhered to then you will get problems and high currents flowing in the primary and secondary but, magnetization flux will remain largely as it was when driven with a single excitation voltage.