Axle that is there now is 12mm.
Between the flat sides? (this is the narrowest part, and the dimension taht determines dropout size and thus axle size that fits in it).
Pretty much all of them (outside of motorcycle/car/etc sized motors) are 10mm between the flats, and that's the dimension that matters.
I ask if the 10mm QR axle is strong enough because the cyc mid drive kit is 6kw and I will be running a 72v battery that can deliver 90amps continuously and 120 Amp bursts.
What hardware do they recommend having? Or what minimum hardware do they require?
My guess it it's strong enough. I use a QR axle on the front of the heavy heavy-cargo trike SB Cruiser, and it handles the braking forces stopping a few hundred pounds of trike, me, load, etc (over half a ton of weight with some of the biggest loads carried on the trailer over the years). I dont' know the math, but I'm sure there's a way to find out how much force that places on the axle, and the same math should be able to see how much force your gearing and that motor would put on your QR axle.
I'd be more worried about the OEM parts of the bike itself, if it has suspension pivots, etc., as thsoe are usually plastic bushings rather than bearings, etc. The pivot bolts are probably metal, but they probably don't fit the holes precisely. Between these two things the chain pulling may force the frame sideways at the right rear during accelerations, and wiggle the rear end back and forth from this repeatedly, wearing the bushings / pivots faster than usual (or even damaging them if suspension is in action during the lateral movements and those are hard enough).
I've added a Pic of my drop out.
You'd have to actually see / measure / etc the dropout itself, rather than all the installed hardware on it, to know what it is; waht size axle it can hold, etc.
It does appear to have a torque plate built just to hold the axle in the dropout, so if the dropout itself is a big hole behind that, youc ould make your own version of htat TP to be a dropout for whatever axle you want to use in there, assuming it's made the same way on both sides of the bike. .