71 Duster 340 carb issues? Maybe

Get a good flashlight look down the primary barrels of the carburetor as you give it a couple quick pumps you should have a strong flow of fuel from the accelerator pump. You could also put a clear fuel filter in the line near the carburetor to assure you of adequate fuel to the carburetor. Also check the site bowls after it's been running to make sure that you don't have a float problem. Do this with the motor off after running for a while.