Will this circuit function properly? (Toggle Flip Flop)
Why this circuit doesn't work/can't work as a toggle flip flop.



Pressing T1 will short Q1 collector-base reducing Q1 to a diode. Current can then flow through R1, base-emitter Q1 and LED D2 causing the LED to light up. D1 is reverse biased and will not conduct.

Release T1, Q1 is off and D2 will extinguish. There is no latching function.

Press T2 and current flows through R1 but nothing else happens.

Press T2 and T1 simultaneously and T2 shorts across Q1 and D2 - nothing happens.

Effectively your circuit is just a battery, resistor, PTM switch and LED in series.

If it won't work, how could I rewire it to function properly? 

Start again from scratch and research how BJTs work and how latch circuits work.