[dmjlambert]

This is how I understand it.

The stock setup is: Air flows into the snorkel of the air cleaner housing, goes through the air filter and down into the spacer between the air cleaner housing and the carburetor (shown in the picture in the top message of this thread). Most of the air goes down into the carburetor, but there is a hose connector on the spacer to send some of the filtered air to the passenger side valve cover. During a backfire situation, you don't really want flames going down that path and into the valve cover, so you put a flame arrester there at the valve cover.

If you don't have a stock setup and you get filtered air from somewhere else, such as from a stand-alone breather filter getting air from the engine compartment, then you would not need a flame arrester. If you're getting air from the air cleaner that is attached to the carburetor, that is when you better use a flame arrester. The fumes in the crankcase include blow-by and are flammable.

To continue the journey (for either stock or non-stock setup), the air that goes in the passenger side valve cover goes through the crankcase (to give it some positive crankcase ventilation) and gets sucked out of the driver's side valve cover via the PCV valve, and into the large vacuum port at the front of the carburetor.