I purchased a Z Bar reconditioning kit recently. There were two circular shaped felt pads included. I installed one on the drivers side of the Z bar but don't see where the other one goes if anywhere? Was this an extra?

Perhaps on the engine side ball stud?

1968 Camaro with small block 35o is the vehicle.

Thats right, engine side. They work like dust boots.

Between the ball stud and the Z bar like a friction cushion? I'm getting a noise when the clutch is depressed. I have lubricated the ball stud, zirk fitting clutch linkage rod, etc. and still the noise. Should the pad install take this away?

These are dust seals,, no friction ablilites... The noise could be coming from something hitting the fork, release bearing dry, etc... Get someone to depress clutch and look at linkage to see if its not hitting exhaust or steering arm. Car needs to be jacked up on stands for safety and two people are required. You should have some return springs attached. Is fork hitting firewall?