Okay, let's face it, this team needs some reworking.
Why Fling on Infernape? While it's true that it hits Psychics hard, Fling is a one-time move. Mulch also doesn't do much damage when Flung. Infernape also has a wide movepool, so you should take advantage of it:
-Overheat/Fire Blast
-Close Combat
-U-turn/Grass Knot
-Stone Edge/Mach Punch
Nature: Hasty/Naive
EVs: 252 Atk/64 SAtk/192 Spe
Item: Life Orb
or
-Nasty Plot
-Fire Blast
-Close Combat/Focus Blast
-Vacuum Wave/Grass Knot
Nature: Hasty/Naive
EVs: 64 Atk/252 SAtk/192 Spe or 252 SAtk/4 SDef/252 Spe
Item: Life Orb
or
-Swords Dance
-Flare Blitz/Fire Punch
-Close Combat
-Stone Edge/Mach Punch
Nature: Jolly
EVs: 252 Atk/4 SDef/252 Spe
Item: Life Orb
or
-Fire Blast/Flamethrower
-Close Combat
-Grass Knot
-Hidden Power (Ice)
Nature: Hasty/Naive
EVs: 64 Atk/252 SAtk/192 Spe
Item: Life Orb
or
-Flare Blitz
-Close Combat
-Stone Edge
-U-turn
Nature: Jolly
EVs: 252 Atk/4 SDef/252 Spe
Item: Choice Band
While Weavile is viable in OU, it's prone to priority from Scizor, who inflicts massive damage with Bullet Punch. Infernape can take care of Scizor. Also, Weavile's STAB moves are tied down to its much weaker Special Attack, so you have to give it all physical moves:
-Pursuit
-Ice Shard
-Low Kick/Brick Break
-Ice Punch/Night Slash
Nature: Jolly
EVs: 40 HP/252 Atk/216 Spe
Item: Choice Band/Life Orb
or
-Swords Dance
-Night Slash
-Ice Punch/Ice Shard
-Low Kick/Brick Break
Nature: Jolly
EVs: 40 HP/252 Atk/216 Spe
Item: Life Orb
IMO, Shiftry is better off in Sun teams, where it can abuse its Chlorophyll ability. Roserade makes a nice filler in its place; it hits harder than Shiftry and is slightly faster (outside of sun):
-Toxic Spikes
-Sleep Powder
-Leaf Storm/Energy Ball/Grass Knot
-Hidden Power (Ice/Fire)
Nature: Timid
EVs: 4 HP/252 SAtk/252 Spe
Item: Focus Sash
Ability: Natural Cure
or
-Spikes
-Grass Knot/Energy Ball
-Hidden Power (Fire/Ice)
-Stun Spore/Rest/Leech Seed
Nature: Calm
EVs: 252 HP/120 Def/136 SDef
Item: Leftovers/Black Sludge
Ability: Natural Cure
or
-Leaf Storm/Energy Ball
-Sludge Bomb
-Hidden Power (Ice/Ground)
-Sleep Powder/Spikes/Toxic Spikes
Nature: Timid
EVs: 4 HP/252 SAtk/252 Spe
Item: Choice Scarf (Sleep Powder only)/Life Orb
Ability: Natural Cure
Palkia is an Uber Pokemon, which means it can't be used in OU. Kingdra is a non-Uber alternative to it despite its lower offensive capabilities compared to Palkia, but it compensates with its good bulk:
-Dragon Dance
-Waterfall
-Outrage
-Rest
Nature: Adamant
EVs: 144 HP/160 Atk/40 SDef/164 Spe
Item: Chesto Berry
Ability: Swift Swim
or
-Substitute
-Dragon Dance
-Waterfall
-Outrage
Nature: Adamant
EVs: 4 HP/252 Atk/252 Spe
Item: Leftovers/Lum Berry
or
-Dragon Dance
-Waterfall
-Outrage
-Ice Beam/Hydro Pump
Nature: Naughty/Naive
EVs: 252 HP/32 SAtk/224 Spe
Item: Life Orb
or
-Rest
-Sleep Talk
-Dragon Dance
-Outrage
Nature: Adamant
EVs: 252 HP/60 Atk/196 SDef
Item: Leftovers
Ability: Swift Swim
If you want to use Palkia, make the most out of its huge offensive movepool. Heal Block doesn't cut it; while it's tempting to prevent opposing mons from using Rest, Recover, etc, Palkia is better off just smashing stuff instead:
-Spacial Rend/Draco Meteor
-Surf
-Thunder
-Outrage/Fire Blast/Draco Meteor
Nature: Hasty/Timid
EVs: 4 Atk/252 SAtk/252 Spe
Item: Choice Scarf
or
-Surf
-Spacial Rend
-Aqua Tail/Outrage
-Thunder/Fire Blast
Nature: Hasty
EVs: 4 Atk/252 SAtk/252 Spe
Item: Lustrous Orb/Life Orb/Haban Berry
or
-Aqua Tail
-Outrage
-Spacial Rend
-Fire Blast/Thunder
Nature: Hasty
EVs: 252 Atk/4 SAtk/252 Spe
Item: Lustrous Orb
or
-Surf/Hydro Pump
-Spacial Rend
-Draco Meteor
-Thunder/Fire Blast
Nature: Timid/Modest
EVs: 4 HP/252 SAtk/252 Spe
Item: Choice Specs
or
-Substitute
-Focus Punch
-Spacial Rend
-Surf/Thunder/Fire Blast
Nature: Hasty
EVs: 100 Atk/156 SAtk/252 Spe
Item: Expert Belt/Leftovers
or
-Aqua Tail
-Outrage
-Earthquake
-Stone Edge/Dragon Claw
Nature: Jolly
EVs: 4 HP/252 Atk/252 Spe
Item: Choice Band
or
-Bulk Up
-Aqua Tail
-Outrage
-Earthquake/Dragon Claw
Nature: Jolly
EVs: 4 HP/252 Atk/252 Spe
Item: Lustrous Orb