Eureka!
Poliwrath
(https://img.pokemondb.net/sprites/black-white/anim/normal/poliwrath.gif)
Surf
Waterfall
Wake-Up Slap
Ice Beam
Item: Amulet Coin
Ability: Water Absorb
Nidoking
(https://img.pokemondb.net/sprites/black-white/anim/normal/nidoking.gif)
Poison Jab
Strength
Stone Edge
Return
Item: Soothe Bell (Will not have one until Togepi evolves)
Ability: Poison Point
Typhlosion
(https://img.pokemondb.net/sprites/black-white/anim/normal/typhlosion.gif)
Flamethrower
Sunny Day
Solarbeam
Swift
Item: Charcoal
Ability: Blaze
Gengar (Will be Haunter until National Dex)
(https://img.pokemondb.net/sprites/black-white/anim/normal/gengar.gif)
Shadow Ball
Confuse Ray
Dark Pulse
Sludge Bomb
Item:Wide Lens
Ability: Levitate
Jolteon
(https://img.pokemondb.net/sprites/black-white/anim/normal/jolteon.gif)
Thunderbolt
Rain Dance
Thunder
Thunder Wave
Item: Magnet
Ability: Volt Absorb
Togetic (Will update to Togekiss after Lance)
(https://img.pokemondb.net/sprites/black-white/anim/normal/togetic.gif)
Fly
Metronome
Magical Leaf
Ancient Power
Item: King's Rock (Will be Soothe Bell until Togepi evolves)
Credit goes to PokemonDB.net for move sets and sprites and blocked.net for held items
The only offensive moves your Jolteon has are Electric type moves. Replace Thunderbolt with Grass Knot, that should give you an advantage against Rock/Ground types if your Poliwrath is knocked out.
Grass knot is crap on Jolteon, seeing as it's Attack stat is so poor, and Jolteon also doesn't get any good Special coverage moves in this generation. And yes, I know I have two Poison Types, but Nidoking was THE BEST OPTION for a ground type.
thunder could use replacing if you're still going for the accuracy stuff. i was going to suggest shadow ball, but gengar seems to have it as a tm instead.. well, if you can nab yourself a second somehow, that'd be a good choice. then again, you do have rain dance, which ups thunder's accuracy.
hidden power could work if it gets you a nice typing. uturn if you're going for smth less offensve - jolteon's speed makes it a nice scout. protect also
I just beat the 3rd gym, and Whitney was a complete joke. Used Togepi to kill Clefairy and switched to Gastly to put Hypnosis and Curse on Miltank then stalled it out.
UPDATE
Changed Togekiss to Togetic because the shiny stone isn't available until after the national dex
HUGE UPDATE:
THE RUN HAS CAUGHT IT'S VERY FIRST SHINY!!!!
I was just grinding levels on my Eevee in Union Cave (B1F) When I just run into a shiny!
Unfortunately, instead of Sandshrew, Geodude, or even Onix, I run into this ugly crudder.
(https://img.pokemondb.net/sprites/black-white/anim/shiny/zubat-f.gif)
Who wants it? I don't.