What is wrong with this DC-DC smps desgin
You can't have a flyback diode on the primary of the transformer - it will take all the energy and cause saturation of the core.

You have what is called a "Forward converter" here and there needs to be specific arrangements to reset the flux in the transformer.

It is a "Forward Converter" because the polarity of the windings is such that the diode D2 conducts at the same time as T2 is conducting.

Did you intend to make a flyback converter?

A darlington transistor such as you are showing is probably too slow to function in this circuit.  At a minimum you need a resistor from T2 base to ground to quickly make T2 stop conducting. I would recommend using a MOSFET or an integrated PWM controller such as a MC34063. There are many alternatives available.

It is very difficult to develop such a circuit without an oscilloscope to see what is happening.