Taking some time to review.
Honestly, this is very very confusing. In the prologue, I thought that Chaos was an abstract idea, or pretty much anything that isn't human. Then in the first chapter, Chaos is a woman? Who I think is the Champion of every single region? Which is kind of difficult to be, since it means that she has to travel all across the world a lot for League challenges (and whatever else you believe a Champion's duties are).
It's also confusing to tell just what is going on. For one thing, why does Professor Oak have the Red and Blue Orbs unprotected in
his lab? They should at least be kept in Hoenn, since they're items with the power to summon Legendary Pokemon that can destroy the world. So they need to be heavily protected. Having them sent to another region and then kept in a high-profile place that's easy to get to (a wooden door in the back of an unguarded lab) is just asking for them to be stolen. So I hope Oak isn't shocked by their disappearance.
And why is it Team Rocket that's aiming for Groudon and Kyogre? Both Aqua and Magma were the teams mainly involved with those two Pokemon. I don't even think Giovanni ever wanted those Pokemon. Though I think a lot of back story is missing, since the prologue mentions that Chaos already released the two from Giovanni before, and readers don't know why Giovanni even wanted them. Why would he stretch his resources to Hoenn when he's already got Kanto and Johto covered with their own Legendary Pokemon to destroy the world. It wouldn't make sense for him to stretch out his team, especially if the Champion of all the regions was around. Chaos could find him anywhere.
Chaos had summoned Celebi, taking him to the future.
Why would Chaos do that? Why not keep Giovanni in the same time era so she could keep watch over him? Why send him into the future where technology's better, or where Chaos might not even be around to help? She doesn't know what the future would be like. As I said, she can't even be sure that she would be around in ten years, since she's traveling all over the world anything could happen to her. Ten years is a long time.
Not only that, but how could she let people know that there's a crime lord suddenly appearing from the past who had control over several Legendary Pokemon? How could she let anyone know to keep an eye on Giovanni, except for future!Chaos herself? And if that's the case, why not keep him in the present time where it would be easier to do because
the world currently knows about him and would be willing to help. In ten years, that's history to them, especially if Giovanni suddenly disappeared and wasn't a threat anymore.
It's also questionable why she would keep him in a cave in the middle of nowhere. I guess a Lucario is watching Giovanni, but even that's not enough. There are certainly police officers in cities that could help keep a better eye on Giovanni. Not to mention that a high-security prison is a better place to hold a man who apparently succeeded in destroying the world.
I'm also wondering why Chaos is there to welcome the new trainers of Pallet Town. There are starting trainers from each professor's lab in every region, and in every town in every region. They all don't just start in Pallet/New Bark/Littleroot/etc. Why would Chaos take time out to greet
these three, especially considering she's the Champion of every region and is apparently committed to stopping the evil teams of the regions. Being around these three trainers puts a target on their backs as they stand next to the Champion that perhaps every evil team in the world wants to attack.
It doesn't even make sense that these three new trainers are in the story itself. They don't do anything against Team Rocket. They can't do anything against the Rockets as their Pokemon are very young and inexperienced. And they also disappear by the next chapter because they're just so unimportant. They can't help Chaos, and are only a hindrance because she has to worry about them in the battles. And she doesn't even worry about them anyhow, so it makes the whole thing a moot point because the kids disappear in a paragraph's length of time.
Speaking of the battle, it doesn't say much for the Champion of all the regions to lose to three Pokemon and maybe a handful of Zubats. She's supposedly strong enough to take out the Elite of at least five regions. Elite trainers that the evil teams are afraid of for being stronger than them. It doesn't make sense that the strongest trainer in all the world gets beaten easily by Rocket members (especially if you want to consider that in the games, they're easily beaten by a ten-year-old kid).
And I'll just say that in several canons, Mewtwo escaped on his own. He didn't need the help of humans to escape from Team Rocket's labs. (Except for in the anime short, but he had the reason that he didn't want to fight anyone. Before that though, he was very willing to kill anyone.)
Now before I get to the specific quotable mechanics, I'll continue to cover the general stuff. Namely description. One reason why this was very confusing was because there was no description. Not only of what was going on, but the characters themselves and their motivations. If you took the time to explain what's going on, then there would be less questions about the plot.
Also, describe your battles. In Pokemon stories especially, with ones like this, battles are where the excitement comes from. They're your action scenes. Don't brush over them. You could make the second chapter more exciting if you wrote out the battles. This way, readers could see that Chaos is very dependable as a trainer and believable as a Champion. Without writing out the battle and just saying that the Rockets won, readers are left to question how Chaos could possibly be strong enough to dominate the Leagues in several regions.
Without this description and narration, the chapters are very lacking. Your chapter two is only two paragraphs long. It could easily be stretched out to a few pages with just the battle being written out. (Come on, three Rocket Pokemon and a Champion who most likely has six strong Pokemon? There's plenty of action to write about there.) Never mind that you could raise the stakes and make the reader want to continue on by placing scenes of the other Rocket stealing the orbs during the battle. Taking the time to write that out would again help to lengthen your chapter and make it much more satisfying to read.
Now for any quotes of things to fix.
Chaos had locked him away 10 years ago. Halfway between Kanto and Johto in a cave.
These two sentences should be one, and generally it's advised to write out numbers under 100, so it would be "ten".
Mewtwo was taken off him.
"away from" instead of "off"
"Welcome back, Giovanni," said the Rocket executives..
"Please can I choose first?" asked the boy Darren and grabbed Squirtle's pokeball. Charlotte took Charmander and Liberty took Bulbasaur.
They spun around, startled, and a Toxicroak emerged, followed by a green-haired woman.
revealing a Sandslash followed by a green-haired man
On two pedestals were the orbs of Kyogre and Groudon.
It unleashed a powerful solarbeam, smashing Toxicroak through the wall at Arcanine's feet! Chaos ran through the door - in time to see Giovanni fly away astride Crobat!
Wait, did Giovanni just leave his Arcanine behind?
This felt very rushed. There are many questions related to the plot, some of which could be explained by taking the time to narrate the story. Don't rush through the story. Rushing through the story accomplishes nothing but confusing the reader and turning them away from this story. Take the time to write out what's important, giving your reader time to learn what's happening and taking care of any questions they could possibly have.
It is set 10 years after the 6th story. I have not released the others anywhere yet.
Though maybe if you released the other stories in order, that might help? Then we'd have the back story to Chaos and Giovanni needed to understand this story. And if you didn't want to release them in order, at least take the time to catch the reader up to what's happening.