Using a stone to evolve certain species of Pokémon has been around since ancient times, at least, according to the lore within Pokémon Legends: Arceus, which shows multiple species that need to use Evolution Stones appearing throughout the game.
This means you’ll need to grab at least a few of each Evolution Stone to complete your Pokédex and truly finish your mission. Thankfully, you won’t need to use more than one Water Stone outside of evolving multiple Eevee into Vaporeon for more Pokédex data.
After completing Flaro’s Eevee’s Evolution request, you can choose to grab a Water Stone as a reward. Additionally, you can find them in any area of the game that features breakable blue rocks. All you need to do is have your Pokémon break the rock and there’s a chance it will drop a Water Stone.
There’s always a chance you could encounter a space-time distortion when roaming the region, which has a chance to spawn Water Stones and other rare items inside. Just be careful because there are also dangerous Pokémon inside, too.
As for purchasing options, you can pick one up at Ginter’s Specials in Jubilife Village for 5,000 PokéDollars. Or, if you would rather use the Merit Points you have saved up from returning lost satchels, you can head over to the Trading Post and grab a Water Stone for 1,000 Merit Points.