For one, adjusting the control for one O2 sensor will effect the other due to loading.Why do you have doubts about it?
NickLee could also put a capacitor in series with R4 so that it DOES operate in push pull mode. A couple of clamper diodes on the 555's output would also be in order.Tflyback only system (not push pull) so it wont make any output. So lose the diode. Also with a flyback transformer you only need 1 diode on each output, not a bridge.
The 1k resistor means you get max of about 7mA (prob less) into the transformer and its not an efficient circuit so you wont get much out. I'd drop that to 330 ohms.