Family specific Flawless Battle-stones can be found in the Sack of Pet Supplies obtained from performing Pet Trainer quests, and are Bind on Pickup.
General purpose Polished Battle-stone
Players will have a very small chance to obtain a general purpose and family specific Flawless Battle-stone after winning a match against wild pets; defeating higher level opponents increases the chances of obtaining a stone. Family specific Flawless-Battlestones will be of the same family as the pets that were defeated. These valuable items are not soulbound, and can be sold on the Auction House.