Thanks got the help guys. I really like the ideas you guys gave me.
But as for sylveon, I was checking his learned and breed able moved and it's not listed. How is he able to learn it?
I appreciate your help, this is the first pokemon game I've played since red, and am trying to learn more about competitive play
You have a lot to learn about competitive play, I'm afraid.
As Nymphadora mentioned, use a Dual Screen set for Espeon, as this is its best bet outside of Baton Pass teams:
-Reflect
-Light Screen
-Psychic/Psyshock
-Hidden Power (Fire)/Baton Pass
Nature: Timid
EVs: 252 HP/4 Def/252 Spe
Item: Light Clay
Ability: Magic Bounce
Curse only benefits Payback. Speaking of Curse, it needs a lot of support to work effectively, and Umbreon is better off giving Wish support:
-Wish
-Protect
-Foul Play (Gen V move tutor move)
-Toxic/Heal Bell
Nature: Calm
EVs: 252 HP/4 Def/252 SDef
Item: Leftovers
Ability: Synchronize
Hydra-Rest isn't viable on Vaporeon anymore, due to the nerf to Drizzle. It's even worse when it's combined with manual Rain Dance:
-Wish
-Protect
-Scald
-Ice Beam/Toxic/Roar
Nature: Bold
EVs: 248 HP/252 Def/8 SDef
Item: Leftovers
Ability: Water Absorb
Flareon is considered the worst of the Eeveelutions, due to its shallow movepool. This is the best it can do post-Bank:
-Flame Charge
-Facade
-Superpower (Gen V tutor move)
-Flare Blitz/Protect
Nature: Adamant
EVs: 252 Atk/4 Def/252 Spe
Item: Toxic Orb
Ability: Guts
Dig is too easy to play around, so even though it gives Leafeon coverage against Steel Pokemon, it's not worth it:
-Swords Dance
-Leaf Blade
-Double-Edge/Return/X-Scissor
-Heal Bell/Baton Pass
Nature: Jolly
EVs: 160 HP/124 Atk/224 Spe
Item: Leftovers
Sylveon can only have Pixilate from a Hidden Ability Eevee (Anticipation in its case; it can be obtained from a Friend Safari). It can also learn Wish via egg move, as can the other Eeveelutions. Also, here are better Sylveon sets for you to try:
-Wish
-Protect
-Moonblast (with Cute Charm)/Hyper Voice (with Pixilate; it only affects Normal moves, not ones that are already Fairy type, also a B2/W2 tutor move)
-Shadow Ball/Hidden Power (Fire)
Nature: Bold
EVs: 252 HP/252 Def/4 SDef
Item: Leftovers
or
-Calm Mind
-Moonblast/Hyper Voice (see above)
-Shadow Ball
-Hidden Power (Fire)/Psyshock
Nature: Modest/Bold
EVs: 252 HP/252 Def (Bold) or SAtk (Modest)/4 Spe
Item: Leftovers