Politoed - Ice Beam is better coverage than Psychic IMO. Other than that it seems like a good, standard rain setter. I think it's also relevant to note than rain will probably be pretty popular this season, because both Tyranitar and Hippowdon got banned.
Kingdra - Put 4 EVs in Defense or Special Defense, there's no reason not to. Also, you might want to consider running Timid over Modest for the mirror, but I agree Modest is probably better considering that Kingdra outspeeds almost everything anyways, especially after the ban of Dragapult.
Amoongus - Honestly, I think you're Amoongus is fine. I think it's definitely better than Clefairy on this team as redirection support because it has access to Spore and resists both lightning and grass. Clear Smog can be helpful, too.
Barraskewda/Blastoise - I don't think you need 3 rain sweepers. I think Toxtricity might add more to the team because it can hit opposing rain teams super effectively. Although unconventional, Jolteon might even be worth considering, because of its speed. Jolteon is actually run on Wolfey Glick's new series 6 vgc team, so it has that going for it too. TBH Toxtricity is most likely a better fit for your team because of punk rock + throat spray, and you don't have to worry about Incineroar Throat Chopping you anymore. Here's a standard Toxtricity set:
Toxtricity @ Throat Spray
Ability: Punk Rock
EVs: 252 Spe/252 SpA/4 SpD
IVs: 0 Atk
Hex might be better than Nuzzle, because it goes well with Amoongus.
BTW, whichever rain sweeper you don't cut (if at all), whether it's Blastoise or Barraskewda, don't forget to give it 4 EVs in either Defense or Special Defense.
For the last slot, I would probably suggest Arcanine.
Arcanine @ Safety Goggles
EVs: 252 HP/252 SpD/4 Def
Keep in mind Flare Blitz's damage will be reduced by the rain.