Briggs flywheels normally have two untapped holes on the top surface. The holes are the correct tapping diameter for 1/4" UNC screws. They recommend that you just screw two thread-cutting 1/4" UNC screws into the holes. Personally I haven't found those screws for sale in Australia, and I tap the holes with a 1/4" UNC plug tap. You then pull the flywheel easily with a simple home-made flat plate puller and a pair of ordinary hardware store screws:
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You only have to tap each flywheel once of course - after that it's easy.