Unfortunately it is one of those things you have to experiment with. Thick enough to grab hold of the flint but not so thick that you cannot wrap the lead around the flint or the screw is not long enough to properly tighten the jaws. About the same thickness as your leather should be a good starting point.

Another benefit I found when using lead is that my flints held up longer. With leather the flints would always chip. With the lead not only did I get better sparks but because the flint was held more firmly it did not chip as badly or as quickly.

I no longer use leather if it can be avoided.