The post mount version works the same except the caliper mounts to frame or fork directly through the caliper holes. For 160 front and 140 rear, no adapters are needed. For bigger rotors, you will need the adapters.

What is post to mount?

Post mount is two bolt holes that bolt into the fork parrallel to the wheel. IS mount is two bolt holes where the bolts go at 90 degrees to the wheel (which is what I suspect your J2s are).

Can I use post mount calipers on a flat mount frame?

Any brand of adapter for post mount calipers on a flat mount frame should do the job. Just remember that the adapters for front and rear are not the same.