Why is my Chevorlet Caprice Classic running fine on the highway but shuts off when I slow down to stop in traffic?

Sounds like a vacuum leak / air intake related possible concern. I do not suspect is is a "fuel line issue". Start by checking base fuel pressure and making sure there is no fuel pressure bleed down. If all is good there, check for any vacuum leaks, any air intake leaks. If too much air is getting into the engine when stopped -- you can stall.