No you can't use a flywheel diode on the coil. You want all the back-ENF energy to go to the sparkplug.
I would put a resistor in series with C1 so the pair acts as a RC snubber to limit Q1 peak Vce. And use a 1500v Vce minimum rated transistor for Q1.
Your 300v zener pair will likely destroy itself, so remove it or put a resistor in series, personally I would remove it (once you have the RC snubber sorted out).
You should run a filtered DC supply for Q2, so I would add a small resistor and large cap after the diode, to give about 10-11v DC wihtout any noise from the 12v rail being present.
R5 and R4 are too low, a few hundred ohms would be better. R3 and base resistor values probably need to be adjusted.