I have to replace the flywheel ring gear and starter drive on my 12.5 HP B&S. Do I need to buy the flywheel puller or can you get that flywheel off like the smaller B&S engines by pulling up on the flywheel and having someone tap on the mounting nut loosened up near the end of the threads ?

yep, if the ring gear needs replacing, i wouldn't worry about messing it up. work yourself around as you go, also check the flywheel key for any worn sides while your there.

Thread a nut on the end of the shaft before you start whacking with a hammer or use a rubber hammer, or both to keep from "mushrooming" the threads on the shaft.

Good luck,
Doc