I only use leather. Here's what the leather has to do, as far as I'm concerned.
The leather has to be thick enough to allow the teeth in the top and bottom jaws of the cock to embed themselves without completely piercing, even under the pressure of being screwed done tightly against the flint. And the leather has to be thick and tough enough to be compressed into the nuances of the irregular surfaces of the flint, and every one of them is different. What works for me is the tops of leather work gloves. It is a split cowhide or maybe horsehide (rough both sides) a little over 1/16" thick. I usually cut several at a time to a pattern that works in each lock, and store them in the bag that is designated for each rifle/gun. The best advice would be to change the leather every time you change a flint, but I admit, I don't do that. Still, I don't let them get too old before I put in a new one.
Lead, and I've tried it, tends to not have the shock absorbancy of the leather, and flints tend to shatter. Anyone who has knapped igneous rock into tools and projectile points understands the properties of the leather support/pads. Nothing works better than leather.