the best pouch is maybe no pouch at all - ie a split pocket with either a braid or bowline loop.

i find it works better than a pouch and it's easier to make

sv

Fellow slingers, 
Leather certainly seems to be a popular traditional material but suitable thickness can be hard to come by. Possible sources are leather work gloves; riggers gloves can be very soft and the palm is usually in one piece. Welders gloves are often made from split leather which can be a bit more rigid. Old welders aprons will make hundreds of pouches.
However you may find it easier to use synthetic materials such as old webbing from car seat belts which can be had for free and is indestructible. Some conveyor belting which may be suitable is used in mail sorting machines. Check belting suppliers for new or talk to the tehnical services people in mail centres. They throw out the old stuff by the metre each day. Makes excellent slings!
Good luck, Aussieslinger.

I got my leather from country/gamekeeper fairs and shows.
there's always a clothing maker or some such flogging off of-cuts for a measily few groats :-)
In the states I reckon you'd definitely get it from the renaissaince fairs. We don't have those in england (at least not the same) 'cos we've got the actual history lmao :-)