legitimately trained so no Dream World, Hidden Power or legendaries
I don't really understand what you mean by that; Ninetale's Drought is a DW ability?
Ninetails @ leftovers
EVs: 252 HP, 128 Def, 128 Speed
~ Roar/ Hypnosis
~ Solarbeam/ Substitute
I would rather do defensive with Ninetales, in the senario that you're facing another weather team. If you are, and Ninetales faints early in the game, the other weather type will prevail and since you've built your team around weather, you will be easily swept.
Arcanine @ Life Orb/ Leftovers
Ability: Flash Fire
EVs: 252 Atk, 252 Speed, 4 HP
~ Flare Blitz
~ Wild Charge
~ Extreme speed
~ Morning Sun/ Close Combat/ Crunch
I went with a physical set for Arcanine to abuse its slightly higher attack stat. Life Orb Arcanine would probably suit your team best, since you want a full out offensive. Morning Sun is an option to maybe prolong its time in battle, but if you wanted more coverage, go with Close Combat/ Crunch.
I would put Flash Fire over Intimidate for Arcanine, because you also need to take into account other sun teams you might face. With a full out Arcanine, you don't expect that you will stay in for long enough that the opponent will do significant damage to you, so Flash Fire over Intimidate.
Infernape @ Life Orb/ Choice Band
EVs: 252 Atk / 252 Spd / 4 HP
~ Close Combat/ Mach Punch
~ Stone Edge
~ Fire Punch/ Flare Blitz
Standard set for Infernape.
Shiftry @ Life Orb
EVs: 252 Sp. Atk, 252 Speed, 4 HP
~ Giga Drain
~ Dark Pulse
~ Nature Power/ Sucker Punch
Sucker Punch > Fake Out because of STAB; Fake Out might flinch the opponent, but it's useless after your first turn in battle. I feel that Sucker Punch is best in case, idk, a Jumpluff outspeeds you in the sun. Growth will be better in Sun, since it gives you 2x Atk and Sp. Atk boost, which will also boost Sucker Punch. I know that Giga Drain doesn't seem to be a very powerful move (base 75) compared to Solarbeam, but with Growth, Life Orb and STAB, it will do enough damage to a water type to cripple it while healing you.
Salamence @ Life Orb
Ability: Intimidate/ Moxie
EVs: 252 Atk / 252 Spd / 4 HP
~ Draco Meteor
~ Fire Fang/ Fire Blast/ Aerial Ace
Mixed Sweeper; might as well abuse Draco Meteor. You can either cover your Bug/ Grass/ Ice types with a fire move, or cover Bug/ Grass/ Fighting types with a flying move, your choice. I don't particularly feel that Aerial Ace is worthwhile on Salamence, especially with Life Orb, because of the relatively low damage that it deals. You might as well go for a STAB Dragon move instead.
Swampert @ Leftovers
EVs: 252 HP, 252 Atk, 4 Def
~ Ice Punch
~ Stealth Rock
Bulky Sweeper; Stealth Rock is a good option because it will negate opponents with Sturdy, so you can sweep w/o damage dealt.
I think you should consider a rapid spinner; 3 out of 6 of your team have a x2 weakness to rock, so consider a Pokemon that clears entry hazards (such as Starmie/ Hitmontop) while also dealing damage.