I need guidance on designing a 2 kV capacitor charging circuit
Not sure what circuit topology that is - it's missing essential parts of both a flyback and a forward converter.
First, some numbers.  When fully charged to 2 kV, a 50 uF capacitor holds 100 W-s (watt-seconds) of energy.  To replace that in 0.1 s requires a 1 kW power source; in 50 ms it is a 2 kW source.  A 2 kW boost converter is a significant design task for an experienced power system designer, and way beyond a student.  I'm not picking on you here, just putting things in perspective.
Separate from that, if this is just a classroom exercise, your approach has problems.  While Q6 and Q7 (seriously, THANK YOU for using reference designators) charge up the transformer primary, there is no mechanism for reversing the direction of primary current to reset the transformer core and for the secondary.  The diode-and-capacitor stuff on the secondary looks like a Cockroft-Walton circuit, but if so it has connection errors.
https://en.wikipedia.org/wiki/Cockcroft%E2%80%93Walton_generator
Also, for a C-W circuit consider the current through the capacitors.  At 4 kHz, a 1 uF capacitor has an impedance of 40 ohms.  At 1 A of secondary current, there will be significant voltage drop across them.
Also, most importantly, a C-W circuit requires a symmetrical AC waveform to drive it, one with (hopefully) equal source impedances for both directions of electron flow.  This requires symmetrical drive of the transformer primary, which your circuit does not have.  As above, it drives the transformer primary in one direction only.  As a basic starting point, look at a Royer oscillator circuit.  This is very popular in UPS designs, which is essentially what you are building.
https://en.wikipedia.org/wiki/Royer_oscillator