I have a briggs and stratton 3.5hp flathead mower engine. It starts but dies after a few seconds. It backfires through the carb and a barely any compression. Do I need to regrind the valves? Please help. Thanks

First make sure the woodruf key on the flywheel isn't sheered off.

Hi,
Sounds as if you may well have multiple issues involved. The valves definitely sound like they are one of them. Removing them, lapping the valves and seats and setting the valve stem to tappet gap. My favorite gaps are 0.007"(lightly snug) on the intake and 0.010"(moderately snug) on the exhaust. Clean the head and the top of the piston before installing it and a new head gasket. Torque in three stages to 165 in./lb. by starting with the bolt between the valves and jumping across to the opposite side, torquing it, go adjacent to it such that the next jump will be at the corner nearest the exhaust, torquing it, jump and repeat alternately jumping and moving beside. I generally go 55 - 60 in./lb. 110 - 120 in./lb. and the final step to 165 in./lb.
You do not state the age of the engine though it would be thirty years old or more to still have contact points which do go bad. A partially sheared flywheel key will result in poor performance.
I would be unsurprised if you did not need a new diaphragm for the fuel system. Proper cleaning and oiling of the air filter, or replacement and oiling, should be considered as a must as well.
Peace,
Clarke