Cooley, I don't think there is any right or any wrong with lining a strap for your pouch. Hunting pouches vary from one maker to another. Straps were made from what ever was available. If you wanted to double your strap I see nothing wrong with that. I usually make my straps from one long piece of leather and a shorter piece of leather with the buckle attached. I have made bags with one solid piece of leather and some made from several pieces of leather. In the March/April addition of Muzzleloader Magazine, Tim Albert's article is about making a pouch. The strap for that bag is made out of multiple pieces of leather. Sure go ahead and double your strap, I see nothing right or wrong about that.
Kind Regards
Frank Barker