Even though Jerry is a hard rock axeman, his sound tends to come from music other than traditional metal or rock. If you really want a signature Jerry Cantrell sound, pick up a Cantrell Signature Crybaby Wah, or listen to some of Alice In Chains material when Layne Staley was the lead singer. His vocals went off the beaten path, and weren't hard rock tinged. They tended to be blues and soul based.
That's how great Layne was as a singer. I wish he was still here. I think you'll enjoy listening to Jerry.
If you want more insights from Cantrell I'll have some lessons from him.
So go back and listen to AIC's Facelift album from way back.