Why does engine shutter with burnt rubber smell?

check for failing drive belts and check for a pulley that is running hot or reluctant to spin freely

The louder noise and burnt smell possibly was the bearing getting worse, or going out, causing the belt to slip over the pullet and start heating up.
Was it a burnt rubber smell?

I don't see how this could have anything to do with the flywheel though.

maybe your altornator belt?

If the smell is like burning oil or really hot coolant. you may have killed the motor. If it smells like burning plastic ,look for shorthing wires around the exhaust manifold battery, alternator or place that a wire could be burnt. If a rubber smell check for belt failure.

Sounds like your rear brakes aren't releasing quick enough, and the burnt smell of rubber would be your rear tires almost skidding on the ground without making the screeching sound.

If the pump is starting to seize up, the belt maybe slipping on the pump pulley, causing the burnt rubber smell.

a rubber smell?? the best thing you can do is diagnose it properly by blocking it up high enough of the ground and let it smoke then slide yourself under there and see where it originates ... check for witness drip marks on the exhaust first??

You may have a frozen bearing on the tensioner or belt idler. This will cause the belt to burn and smell. I think you are on the right track. I would remove the belt and spin the idler and adjuster by hand to see that they are free and don't have excessive play in them. Replace as necessary.

I expect that you have an oil leak that is dripping/running on to the exhaust. The burnt oil will smells a bit like rubber. Check for oil leaks that are higher up on the engine. (Valve Cover gasket for example).

Check serpentine belt, the radidator hose , the air conditioner compressor and also the differential seal they common cause for rubber smell.

Check for any rubber part that can be in contact with exhaust system and inspect wirings looking for shorts.

Also ensure that the smell is not coming from a bad tyre, and check for oil leaks in your engine, burnt oil can be confused with rubbere smell.