Now find a plastic bag around this size or just cut one to size and insert into in between the layers. Don't worry about breath-ability since dogs don't sweat through their skin like us humans, they only sweat through their paws. In essence this vest will help them cool down by "sweating" the water that we soak the upper layer with.
I guess since we have the waterproof layer this may act as a doggy raincoat as well to some extent. Bonus!
UPDATE: You can also add another layer of fabric on top of the bag for extra water capacity or a thin spongy foam (like mattress topper) to help soak in more water as well so you don't have to re-drench it as often on really hot dry days.