Um... Alright. This seems like it could use a lot of work, so I'll start off by quote-reviewing it.
Okay. Several issues here. First of all, I and likely many others would consider it too short. A prologue is an introduction to the story, which you gave, but normally they are expected to be... well, longer. I like how it takes place in the future of the fic itself, though. I'll give you that.
So, this is his definate appearance? He goes through this story as a trainer for at least eleven years and he always wears the same shirt, shorts, hat, and necklace? This is really not a good way to describe your character in the story, either. Just coming out and saying what they wear/what they look like in the first paragraph makes it seem like you're reading a biography-page on Wikipedia or something. Why not describe him looking in the mirror that morning, or putting on his hat, or use another more creative means to let us know how he appears. Don't just tell your readers. Show them. Describe.
You do realize how boring this is to read, right? This single sentence could have been made into even a whole chapter, full of lush detail describing the main character's excitement as he opens the Pokeball and sees his new Squirtle for the first time, the emotions of sadness when he bids his mother farewell, and a load of other things. We should be feeling Fire Eagle's emotions as you show us with your words what he is experiencing.
Not to mention, what does Squirtle look like? I cannot stress this enough while reviewing fanfics. So what if most readers will know all about Pokemon? Fanfiction should be written with the author imagining their readers as people completely unknowledgable about Pokemon (or whatever the fic is about). Meaning, think of how you would describe Squirtle's appearance to somebody who had no clue what a Squirtle, or any Pokemon for that matter, was? This makes the fic more interesting, believe it or not, because the reader can actually place themselves in the story and imagine what it would be like, even when it involves things they've never seen in reality before like blue turtles who posess water abilities.
The battle between Squirtle and Pidgey was done so Fire Eagle threw a pokeball at it and it was a complete catch.
Hold on. Where was the battle? Where was the action? You mean to tell us that you're just going to say "Pokemon A attacked Pokemon B and Fire Eagle captured Pokemon B" throughout the whole fic? That's not interesting at all! Why write a fic if you're not going to at least try to get readers to enjoy it? In Pokemon fanfiction, battles are the main part of the action. They're your chances to get the readers hooked and excited. You can't just skip over them and expect your story to get pleased reviews. And yet again, what does Pidgey look like?
So some complete stranger just gave Fire Eagle an item for no reason? Where's the conversation? There's something called dialogue that allows you to narrate conversations, in case you were wondering. It would have also been useful when Fire Eagle got his Squirtle from Prof. Oak and said goodbye to his mom. It's something that actually gives characters personality and makes them more fun to read about.
What was the "pokecenter" (Pokemon Center, it should be) like? How did his Pokemon get healed? How long did it take? Was anyone there to help him? As far as we know, he could have just walked in, sent out his Pokemon, and magically healed them himself before leaving.
Something else I noticed in your style of writing came up while I read this part. You need to keep in mind: This is a fanfic, not a diary of your playthrough of Fire Red/Leaf Green. A fanfic should be like a book. In a fanfic, you should let the readers know what Viridian City is like, how long he was there, if anything interesting happened, who he met while he was there, et cetera, et cetera. This is not at all descriptive as it should be.
In a forest setting (which we have no image of in our minds right now), this kid sees a Pikachu. Before even telling us what a Pikachu looks like, and without any mention of a battle, he throws a Poke Ball and captures it. See the previous quotes for my reasons why this is such a big deal.
I think I'm gonna stop there, seeing as the rest of the chapter has pretty much the same problems. You need to remember to describe things. Don't expect us to know what everything is.
Also, what I noticed was that none of the characters have any personality whatsoever. What does Fire Eagle really act like? So far, all we can imply is that he's trusting enough to accept items from strangers, likes adventure apparently, and has always been interested in Pikachu. That's not enough to base a character off of, for sure. Is he determined? Shy? Naiive? Laid back? We have nothing to judge that by. Similarly, all of the Pokemon are complete Pokebots. A Pokebot is a Pokemon character in a fanfic that has no emotion or personality; it just does attacks when its trainer tells it to and is otherwise comepletely unimportant to the story. The fun thing about Pokemon fanfiction is that you have fantasy creatures you can give their own individuality. Right now, the only thing that makes Squirtlke/Wartortle different from Pidgey and/or Pikachu is that it uses different attacks and has a different Type. Where's the fun in that?
Don't write a list of events that happened in your playthrough of a game. That's not what fanfiction is about. If you don't like to show us emotion or give us vivid images, then perhaps fanfiction isn't for you. If you do want to attempt that, then I hope you'll take this review as constructive critisism and try to apply it to your fic.
I do want to apologize if any of that came off as rude. But, that's the way fanfictiohn works. If you don't want strict reviews, then don't post it online, no matter how good you think it is. As I said before, it would be great to see you reply with a positive attitude about it. This fic has potential simply because now the readers know by reading the prologue that this trainer will become a great leader. The way you get him there is what will decide how good the fic is, though.
Oh yeah, and don't forget to re-read your work! Go over it in a word processor, use spell check if you have it, and fix as many things as possible. Trust me, it's a hard task, but it makes your fic seem a lot better in the end.