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Dare I ask what version you're playing on? To have Ninetales and Arcanine means you either need to trade or you have one ready to import from Pokemon GO already. As for the team...
Alolan Ninetales(Ice/Fairy) <- covers Grass, Flying, Ground, Dragon, Fighting and Dark, hence is solid against Lance and Bruno, Even does well against Lorelei although there are better options out there with regards to her specifically. If you can get it early enough, it does fairly well against Erika and Giovanni too.
Alolan Golem(Rock/Electric) <- interesting choice I must admit. Defeats Blaine quite easily with its Rock Typing(same with anyone using Flying Types) but otherwise doesn't seem to do well against anyone else. Lorelei would crush it with Water moves(despite being vulnerable to Electric/Rock moves), as would Bruno with Fighting. Giovanni would beat it hard with Ground(x4) so I'm not so sure on this one.
Blastoise(Water) <- Seems to fill the same role that Alolan Golem would against Fire Types while also covering Rock and Ground. Can Mega Evolve so I don't really see any problems with this pick.
Alakazam(Psychic) <- Covers Fighting and Poison quite well so Bruno, Koga and even Agatha aren't going to last long. Granted it'll be a battle of attrition on Agatha seeing as its not Generation 1 anymore(so Ghost will be able to fight back).
Dodrio(Flying/Normal) <- Covers Bug, Grass, Fighting and can be used against Ghost since its immune to those moves. It does learn a Dark Type move but seems to overlap with other Pokemon in your team.
Arcanine(Fire) <- Covers Grass, Bug, Ice and Steel. Pikachu version exclusive Pokemon whose a solid pick, although overlaps with Dodrio on a few.
Overall your team covers Grass, Water(albeit poorly with reciprocal vulnerability to Water), Fire, Rock, Bug, Ground, Flying, Dragon, Ice, Steel, Dark and Ghost. Still leaves Normal, Electric, Psychic, Fairy and Water to a degree. Here's what I'd do:
Spoiler:
Alolan Raticate: Normal/Dark Type covers not only Agatha(Ghost) but Sabrina(Psychic) as well. Eevee(for LGE) could fill this slot but I find Alolan Raticate to be superior due to the Psychic immunity and Dark STAB.
Sandslash: Ground Type covers Poison, Steel, Fire and Electric. Easily handles Lt.Surge, Koga and Blaine.. Acquired on Route 3 in LGP so is an early game option. Alternatively you can do Onix, Golem or Rhydon here but know that what matters is the Ground Typing.
Alolan Sandslash: Ice/Steel Type covers everything that Alolan Ninetales does with respect to Ice. What changes is that Steel covers Ice, Rock and more importantly Fairy in exchange for losing Dark and Fighting Type coverage. Although A.Ninetales is immune to Dragon moves, A.Sandslash resists them thanks to its Steel Typing.
Poliwrath: Water/Fighting Type that you can get before Squirtle. Covers Normal, Water, Rock, Ground, Steel and Dark. Easily handles Blaine, Giovanni and can handle parts of Bruno(Onix). If you like Blastoise or another Water Type, then go with it. What matters is that you have a Water Type to counter Fire, Rock and Ground.
Pidgeot: Flying/Normal Type whose sole responsibility is to counter Bug and Fighting Types but also can lend a hand on Grass. Mega Evolves too. Handles Erika if Alolan Sandslash isn't available while crushing Bruno's Fighting Types. If you opt to go with Blastoise or another Water Type, swap Pidgeot out for Scyther or Butterfree. The Bug/Flying Typing counters Dark, Psychic, Bug, Grass and Fighting.
Pikachu/Jolteon: Electric Type meant to counter Water Types and any Flying Types that happen to fall victim to Electricity. Consider this a reserve counter against Lorelei and an ideal counter against Lance's Gyarados. Pikachu or Jolteon for LGP, Jolteon for LGE.
Unless the article Bob wrote for Daily is wrong, Arcanine is available in LGE if you've caught 5 Growlithe's, not Meowth's. Granted in the long run, it doesn't really matter what your team is. It's just you'll have a tough time against Lorelei unless you use Alolan Ninetales since most of what she has is part Water Type and will shred Alolan Golem due its slow speed(so even its Electric and Rock moves that are Super Effective against her won't do much good if you get KO'd before you can move). Maybe consider swapping Alolan Golem for Magneton so that you get a good counter for Lorelei without being completely vulnerable to reciprocation. The Steel Typing also counters Fairy Types, a positive outcome as I see it.
Hmm Rock/Flying, Grass/Psychic, Ghost/Poison, Water, Fire and Rock/Electric. As I said before, if you're using Alolan Golem to counter Water Types, its going to end badly. If Exeggutor is dealing with Water Types, then what is Alolan Golem's purpose? I suppose countering Flying Types or Bug Types but there isn't a Gym involving those and Vaporeon can handle Flying with Aurora Beam and Arcanine(or Aerodactyl) crushes Bugs. If its to counter Ice, Aerodactyl's speed wins here despite its clear vulnerability to Water and Ice moves. Heck Kabutops would have better luck against Lorelei being a Water/Rock Type since its Water Typing reduces its vulnerability.
I'd reorganize the team again but as I said before, it really doesn't matter what team you use. Having fun and using what you like is ultimately what matters. However, if you wanted a suggestion, here's what I'd go with:
Eevee(Normal Type starter)
Alolan Ninetales(Ice/Fairy)
Ninetales(Fire) or Arcanine(Fire)
Vaporeon(Water) or any Water Type
Exeggutor(Grass/Psychic)
Nidoking/Nidoqueen(Poison/Ground) or something you like(basically a flex play).