Espeon is the most important Pokemon on Baton Pass teams thanks to a combination of its ability Magic Bounce, formidable power, and decent Speed tier. If you are just looking for a Magic Bounce user and not a full Baton Pass team, use Mega Diancie or Sableye on offense and balance or stall, respectively. With STAB Stored Power backed up by Baton Passed boosts, Espeon can sweep a large portion of teams. Nothing beats it one-on-one once it has set up, but it sometimes finds difficulty doing so due to its reliance on hax and its terrible stats. It also requires heavy team support in order to function and is near useless on its own.
Stored Power takes advantage of all of the boosts Espeon's team has Baton Passed to it. Dazzling Gleam is essential coverage for Dark-type Pokemon. Substitute capitalizes on the evasion that is often Baton Passed to Espeon, which allows it to get free Substitutes up. Espeon will also often have numerous defensive boosts, which prevent a large portion of attackers from breaking the Substitute. Baton Pass allows Espeon to continue the Baton Pass chain.
Magic Bounce is Espeon's only viable ability, granting it an immunity to Taunt, phazing, and status. Leftovers gives Espeon passive recovery. The given EVs and a Timid nature allow Espeon to be as fast as possible with maximum damage output.
Early-game, Espeon is used to reflect entry hazards, Taunt, and phazing. Late-game, once your Baton Pass chain is all boosted up, Espeon is used for sweeping. Baton Passing to Espeon against Pokemon such as Klefki and Mega Sableye is a good idea, as it completely walls them. Be careful when bringing Espeon in, as it is often the wincon on Baton Pass teams and if it faints you lose your only way of dealing damage.
Espeon only fits on full Baton Pass teams, so teammates that boost Speed, Special Attack, and bulk reliably are essential. Scolipede and Blaziken are excellent options for passing Speed, as they can also pass Attack via Swords Dance.Zapdos is another great teammate for boosting Speed because it also acts as a reliable answer to Mega Rayquaza. Mr. Mime is an excellent team option because it can pass Calm Mind boosts as well as grant an immunity to Perish Song thanks to its ability Soundproof. A defensive booster such as Acid Armor Vaporeon is very important because of all the priority attacks floating around in Anything Goes. Smeargle is a great partner too because it gets stat boosts every turn thanks to Moody, helping Espeon take advantage of Stored Power, and can afford to run any moves it wants. Drifblim pairs well with Espeon, as it is the most viable Evasion passer, getting Minimize, Substitute, Magic Coat, and an excellent defensive typing, allowing it to deal with most Extreme Killers efficiently. Having two Espeon on a team can actually be very useful, giving you a second wincon and leaving more room for error.
When using two Espeon, a second Espeon set with no Special Attack investment and instead HP investment can be extremely useful for supporting a team so that you don't need to rely on your wincon to also block status moves and entry hazards.
Checks and Counters
Perish Song: Perish Song is the biggest counter to Baton Pass teams; if the opponent has a Pokemon with Perish Song, Espeon's team can often just lose at Team Preview.
Ditto: If Espeon doesn't have a Substitute up, Ditto can come in, copy all of Espeon's boosts, and Baton Pass to a teammate of choice, which can then potentially countersweep.
Haze: Haze removes all boosts, rendering Espeon completely useless. Luckily, Haze is nearly never seen in Anything Goes.
Primal Kyogre: Thunder ignores evasion in rain, which can let Kyogre break Baton Pass early in the game. The chance to paralyze is also annoying. However, if Espeon has had a few Special Defense boosts passed to it, Primal Kyogre loses one-on-one.
Strong Attackers: Strong attackers such as Rayquaza and Life Orb Extreme Killer Arceus are huge threats for Espeon and Baton Pass teams in general, as they threaten to break through boosts and KO Espeon and its teammates before they can finish the Baton Pass chain. However, if Espeon has enough boosts passed to it, it can beat the strong attackers one-on-one.