Tall Hat,
Most folks recommend for a Shot Pouch (18th century terminology), Hunting Bag, Shooting Pouch, Possibles Pouch (or whatever you want to call it) that you use Veg Tanned 3 to 3 1/2 oz./ounce leather.
The following link shows a Weight/Thickness Chart that works with plain Veg Tanned Leather. However, Veg Tanned leather is not an exact thickness throughout the hide or piece of leather and that's why it is normally described as between one size and an additional half ounce, as in the 3 - 3 1/2 oz. size mentioned above.
https://www.tandyleather.com/en/leather-buying-guide.html
I have made shot pouches out of the next size up Veg Tan leather, though I hand work it a lot so it is pretty flexible. Still, that thickness is not as popular with some folks.
After looking at the Shot Pouches you linked, I have another recommendation for leather that originally came from Brown Bear. Tandy calls the leather "Stoned Oil Sides" and the "Dark Brown" color is close to what you linked.
When I went to my local Tandy Leather Store to look at these sides, I was surprised to find the listed Weight/Thickness: 4 to 4.5 oz. to be thinner in thickness than what the above chart lists for Veg Tanned Leather. The reason the leather is thinner is because it already has been dyed, and has Oils and Waxes worked into the leather. Since the Oils/Waxes add weight, this leather is very close to identical to the 3 to 3 1/2 oz. thickness many people like in Veg Tanned Leather.
This leather does not need dyeing and with the Oils/Waxes in it, it won't take further coats of dye. So you must pick out the color you like of the three colors listed. The leather does not feel "Oily" even though it has the Oils/Waxes in it. Oh, this leather will need additional Oiling as time goes by, just like other leathers. I was very impressed with this leather.
BTW, Tandy discounts the price of this leather every 2 to 3 months, so you can get it a bit cheaper then.
https://www.tandyleather.com/en/product/stoned-oil-sides
Brown Bear recommends the Oil Tanned leather as it stands up better in the very wet conditions he lives in. He also recommended the Tandy "Kodiak" Oil tanned sides and I examined those closely in my local Tandy Store as well. Though I liked the weight and "temper" (flexibility) of this leather, it has an embossed pattern on the smooth side that would not be correct for an historic reproduction of 18th/19th century Shot Pouches and other items. When I saw that embossed pattern on the smooth side of the leather, I ruled it out for that reason.
Gus