67 slant with 1920 holley dies when engine heats up and choke opens.

71twister3bytheknee6 said
where the fuel line flair inserts into the carb,I found two small pieces of rubber,I believe,no doubt starving the carb.

Trash pretty much anywhere in the fuel system is going to make problems. The closer it gets to the heart of the carburetor, the more problems it makes. However, it is very unlikely that trash in the location you mention would cause the problem you describe. If it were blocking the flow of fuel, the engine wouldn't run even with the choke closed. I think the carburetor exhibiting that behaviour has some clogged internal passages that need to be cleaned out.

It runs allright,heh,better than the horror stories I have been hearing about refurbished carbs

There's nothing wrong with a properly refurbished carburetor. "Remanufactured" carburetors (and other parts) tend to be junk.

Where the fuel enters the carb,there appears to be a black rubber membrane behind the small (about 1/8 inch) round opening to the carb.

Yes, that's the rubber tip of the inlet needle. It's supposed to be there.

Could any of the small pieces of rubber I found have worked there way in a reverse direction,meaning there is damage to something in the carb?

Probably not.