Something isn't right.
The coils get +12V from the battery - through the ignition switch - and complete the circuit to ground through the points. If you have voltage at the points but not at the coils... well, it makes no sense.
The power (black) wire to the coils comes a long way through the harness, as the ignition and kill switch are involved. The coloured wires for the coils go pretty much directly to the points; the wires attached to the points plate connect directly to one end of each coloured wire, the other ends are beside the coils. There is NO ground connection to the frame at the coil. The iron core is grounded by being bolted to the frame but nothing electrical should be grounded. The primary coil is as above, the secondary (spark) coil connects to a spark plug at each end.
Make sure your coils are around 5 ohms primary resistance measured with a decent ohmmeter, between 3 and 6 ohms at least. Other types of coils for electronic ignition particularly - and Kawi was an early user - may have very low primary resitance and will not work with points.
You need 12V at the black coil wire and a ground on the other wire when the respective points contact is closed. When the points contact opens you get a spark. Both plugs on one coil spark simultaneously so you have to have both plug leads connected to a grounded spark plug to get any spark. Don't operate a coil much with one or both plug wires off, they can spark internally (if there's no other way to discharge) and be ruined.