Number 1. It shows Giovanni with a typical tropical shirt. The palm tree's on the shirt make it a typical Hawaii shirt.
As people have said, the anime doesn't really mean much in relation to the games, but even if we want to, this still means absolutely nothing. The specific image you showed comes from a fantasy the Meowth had about Giovanni. That means that Giovanni may not even own such a shirt, it's just the way Meowth imagined him.
Number 2. In the trailer we saw the beach girl with a slowpoke, in Heartgold Soulsilver Team Rocket sold Slowpoke Tails to make money. It would be fun it this slowpoke shown in the trailer would be a hint back to team Rocket use slowpokes.
Slowpoke was also in the Kalos regional dex, but Team Rocket didn't return in Kalos. Regardless, why would Team Rocket having one plan involving Slowpoke automatically mean they appear where ever a slowpoke does.
Number 3. There is a lot of foreshadowing in the Pokemon game the Team Rocket will return. (A. In Fire Red / Leaf Green B. in Heart Gold / Soul Silver. C. In Black and White 2 )
The grunt from Fire Red/Leaf Greeen that says he will revive Team Rocket is actually meant to Proton from Heart Gold/Soul Silver. It was a clever reference they built in. As for the others, hints at Team Rocket coming back doesn't necessarily mean they'll come back know.
Number 4. The Mossdeep City / Solar System theory. The gymleaders of Mossdeep, Liza and Tate, use a Solrock (sun) and a Lunatone (moon). In Mossdeep there is a Space Station with a Rocket. There is also a place where 'you' can stand on the moon and see the Poke-earth. Interestingly Giovanni hand out the Earth Badge in Gen 1. This could link all of this together. The Sun, Moon and Earth are all part of the Solar System and with the help op Rockets, one can travel from one place to another.
I'm sorry, but that's just ridiculous. You are making connections where none exist. A rocket appearing has absolutely nothing to do with Team Rocket unless a direct link is made by the games. And Giovanni's Earth Badge is not Earth as in the planet, it is earth as in the ground, as Giovanni is a Ground-Type gym leader. On top of all that, there is no way that Game Freak has been planning for Sun and Moon for over 10 years now.
Number 5. The Ghost theory. Phoebe, the Ghost master of the Hoenn Elite Four, is dressed in a 'Alola'-like way. Team Rocket is the only enemy team who had to do something with ghosts. In Lavender Town in Kanto they occupied the Pokémon Tower, filled with ghost Pokemon.
So what? There is literally no link between the two. Even if Phoebe has something to do with Alola, she has nothing to do with Team Rocket. Just because Team Rocket occupied a haunted area one time doesn't mean that they're connected to ghosts so thoroughly that they are now connected to anyone who uses them.
Number 6. This has been recently discovered. In Pokemon X and Y the is a 'Team Rocket Isle', north of the Azure bay. The Rocket 'R' can be seen on this Isle, it looks a lot like the redesigned Rocket 'R' as seen in the anime of X and Y.
That's interesting I suppose, but I fail to see how it means anything. If it is intentional (which it probably isn't) then it's just an Easter egg.
Is this all a coincidence? I don't think so!
I'm sorry, but to call it a coincidence would be too forgiving. It's forcing various aspects that have nothing to do with each other together. The most solid piece of "evidence" you had was hints at Team Rocket's return, but even that doesn't mean anything in relation to Sun and Moon, as it could either be a throwaway line (most likely) or referencing another event that isn't Sun and Moon.
Well that's even more Farfetch'd than the idea that TR is our evil team (which, seeing as we've seen nothing, isn't all as unlikely as everyone wants to argue). Of course "they" knew about GO when making Sun and Moon, but even then, I fail to see how that would inform any decision made in the development of the games.
Hate to say it, but we have literally no grounds to completely discount Team Rocket from being in this game in one form or another. We haven't had a pair of games designed solely for an Anniversary in the main series before, so anything's on the cards until proven otherwise I'm afraid. Even if the reasoning is all over the place.
Sure, it could happen, but is there evidence of it? No.
