It doesn't output AC, not in the usual sense.
Like every flyback, it produces a pulse of secondary current every time the primary current is interrupted. The induced secondary current is turns ratio lower than the primary current which had been interrupted, so for instance a typical 1:100 automotive coil produces 10mA per 1A of input. The secondary current charges capacitance of the winding and external cables until enough voltage develops to strike an arc. During this time, a 100 times lower voltage (so maybe 200~300V) appears on the primary and must be blocked by the interrupting circuit (mechanical switch or transistor).
The primary switching circuit should actually break down and start conducting near this voltage, in order to prevent excessive voltage from appearing on the secondary and damaging coil insulation. BTW, I'm not 100% sure if the limits I give are entirely correct or if lower voltage limit would be safer for the coil or maybe higher could be gotten away with.
The amount of energy delivered into the spark is determined by primary current before interruption, primary winding inductance and "efficiency", which depends on primary leakage inductance and resistive and capacitive losses on the secondary. Total energy in the primary is the usual I²·L/2 and I suppose a large fraction of it is delivered to the spark.
I think your idea of connecting two coils in opposite polarity should work. You will need to ensure that both primaries are interrupted at the same time; this means that transistor drive is the best option.