I have some non-standard bikes to hook up so rather than ordering the kits with fixed length wires, I want to just order appropriate double strand (or coaxial) wire in bulk, along with the connectors, and get the job done that way. I can't seem to find the standard size used for this job, however. Appears to be about 22 AWG.
Won't matter much, 22AWG is rated at about 1AMP for power transmission and 7AMP maximum current (i.e. that is around the current insulation starts to melt), is plenty large enough to carry the current from a dynamo (a few hundred milliamp's) and provides a strong enough wire that it won't break easily when in use. A size or two smaller or larger won't hurt.
The "official" answer is AWG 20.
According to SON (hub dynamo manufacturer), their coaxial cable (and it really is coax, not just 2x conductors inside a round, foam-filled housing) corresponds to:
2 x 0.5 mm^2 conductor wires.
That corresponds, according to conversion tables like this one, to an AWG 20.
As noted above, 22 should already be overkill for the current carried, but in terms of durability of the wire and maybe the crimping at the spade connectors, 20 may be the better bet.
I'm not finding a bulk SON coax seller in the US for < $1 / foot, which isn't terrible, unless you want to do 4 long bikes (as I do) and need about 50 feet, given that bulk auto / electronics 2-strand can be had for a fraction of that price, though it may be a lot uglier.
One more tip if you're going this route, there are spade connector + crimper kits available online (here's an example on Amazon) that give you dozens of the 2.8mm and 4.8mm connectors you need, plus housings for them, as well as a crimper, all for <$30.