I have wound a transformer for exactly this type of application.
8Turns primary 1mm, 50 turns secondary 0.35mm
think its ETD29 Core or maybe the next size
must do it in 3 layers.
First 25T secondary, then that special polyester tape, then 7 or 8T primary, then poly tape,
then 25T sec, tape,
where the wires come out from each layer, put some insulating sleeve on them, some thin
shrink tubing will do,
ensure good insulation, ie tape covering between layers, as voltage breakdown will have consequences, especially the way a flyback works.
The core will need an airgap too, roughly 0.5mm, I use layers of transparency film for this.
maybe should do the primary with 1.2mm wire,
other option is double winding (side by side) of 0.5mm wire - this has electrical advantages, and is much easier to wind.
This one was running at 27khz resonance IIRC
Find a ready made commercial one ?? Good Luck!
As for specs ?
If you have 2 cylinders, running at 6000rpm, => 100 rps
2 firing per round => 200times / sec charging up a 1uF cap
=> charge a cap 1uF to 400V in 1/200 sec