Some tips for each of your members.
Politoed: Seems pretty good, although having both Toxic and Perish Song feels redundant. You also might want to train Special Defense rather than Defense, but that's up to you.
Mantine: As was said above, Mantine doesn't get Hurricane in Gen 7 and Ice Beam as a TM is not yet available in Reborn, so you'll need to swap out those moves. One thing I definitely recommend you have on it is Roost. Mantine got Roost in Gen 7 and it was a godsend for it, pretty much if you're running Mantine you're running Roost too. Also you get Leftovers pretty late so you need a placeholder item until then (remember to not sell your Balm Mushroom).
Magnezone: Again as said above the TMs for Volt Switch and Thunder aren't available yet. Unfortunately that means that you won't be able to utilize the rain for your Magnezone much. Additionally you don't get access to Magnemite/Magneton until fairly late in the game and you aren't able to evolve to Magnezone until even later. If those don't discourage you, then I would recommend against using Zap Cannon since it's super unreliable (you might have meant to say Flash Cannon which is a good choice) and Sunny Day is not great on Magnezone since you'll take even more Fire damage. For replacements I would definitely say use Flash Cannon as it's a really solid special Steel STAB and probably Discharge (maybe replace with Thunderbolt when you get the TM, but that's super late. actually looking at the Rainbow Field effects probably keep Discharge since that would be a 60% chance to paralyze). The other two moves could be pretty much anything you want, if you're running sun on something else then Rainbow Field moves could be useful as was recommended.
Steelix: Steel Roller doesn't exist in Gen 7 and you can't get the TM for Earthquake yet. For a Steel move you'll probably want Gyro Ball since Steelix is pretty dang slow. Nothing in the game is really a good replacement for Earthquake, but the best you can do is probably Stomping Tantrum, and maybe have Dig/Bulldoze or an elemental fang move until you get the tutor.
Infernape: U-Turn and Swords Dance unavailable. If you still want to do physical be aware that the tutor for Fire Punch isn't available until pretty late, so you'll need alternate Fire STAB until then (Flare Blitz is powerful, but it's learned at a high level, though you'll definitely be there before Fire Punch). I'd definitely recommend Close Combat since it's super strong and Mach Punch isn't really enough Fighting coverage. Keep Mach Punch though, and for your last move I would say either Thunder Punch or Bulk Up, both available at/after you can get Fire Punch, or you could use it as your sun setter. (Special is an option too: Nasty Plot, Fire Pledge/Flamethrower, Focus Blast, Solar Beam or something)
Wigglytuff: It's alright. Dazzling Gleam, Hyper Beam, and Heal Bell are all unavailable until pretty late and Copycat is only learnable by Igglybuff at level 11. I would recommend Hyper Voice over Hyper Beam since it's still pretty strong but doesn't require recharge plus it goes through Substitutes, and it's available slightly before you get Hyper Beam. You could run Sunny Day and Flamethrower as was suggested, but even so Wigglytuff isn't amazing and you might be better off swapping it for something with Drought (Torkoal isn't available until pretty late, so you might be better off with Ninetales. You have a 1/18 chance to get a Kantonian Vulpix before the 3rd gym, otherwise you can get it a while later; just be sure to catch a Stunfisk when you get to Apophyll Beach. Also remember to wait until level 42 to evolve it if you want Fire Blast, since the only good attack that Ninetales learns by level up is Flamethrower).
The reason why this would be called a Rainbow team is that in Reborn if you set up Rain and Sun at the same time it will change the field into a Rainbow Field which has all kinds of cool effects, all of which are listed here: https://pokemon-reborn.fandom.com/wiki/Rainbow_Field
But that's pretty much it. Sorry it was a bit long, I went into progressively more detail as I went along. Anyway have fun!