It’s been a while since I reviewed, so I apologize if I’m a bit rusty. *cracks knuckles*
The first thing I notice is that you have some paragraph problems. You don’t have them lumped together in a big wall of text, so that’s good, but remember to double space after every paragraph. Right now, it’s a bit hard to read.
If you double spaced it, your first scene would look like this:
Vincent Cabello sat on the ground, waiting for his mother to come back from grocery shopping. His father, nevertheless, was snoring upon the bed lay upstairs.
Vincent walked into the kitchen, yawning and rubbing the sleep out of his eyes. Slowly, as he heard the creek of the opening cabinet, he remembered that there was no food.
Footsteps were heard on the stairs as his father come downstairs.
“Where is your mother?” he asked.
“Gone, she went grocery shopping.”
“Well—I just heard that Doctor Oak is giving out free Pokémon, you should go.”
“Really?” Vincent’s eyes widened. “I got to get some!”
Vincent dashed outside onto his bike, slipping on his helmet and snapping it in a second, and then he rode off.
See how neater that looks?
Now, for more specific problems.
“Well—I just heard that Doctor Oak is giving out free Pokémon,you should go.”
I thought Vincent’s dad was sleeping. What, did someone phone him or something? And that hyphen seems out of place; a comma would work just find. Also, the second part of the sentence (which I’ve highlighted) has no relation to the previous one, so it should be a new sentence entirely.
As he reached the office, there lay no people.
The highlighted part just sounds weird. I suggest you replace ‘lay’ with ‘were’.
Doctor Oak had three Pokeballs left.
It’s ‘professor’, not ‘doctor’.
“Eevee, Charmander and Squritle.”
What happened to Bulbasaur?
“Have you beaten Brock yet?”
Did Professor Oak say that? Because I have no clue who’s talking.
Doctor Oak warned Vincent. “His tough.”
He’s.
“Here—you’ll need this—too, Vincent.” Doctor Oak threw a watch in his direction, and Vincent caught it, snapping it to his wrist.
Again, hyphens are not needed. Comma can replace the first hyphen and the second can be taken out entirely.
Eevee uses the moves: Tackle, Barrage, Scratch.
Eevee doesn’t learn Barrage. On the contrarily, Barrage is the signature move of Exeggcute and Exeggutor and involves throwing eggs (to my knowledge).
“Abra, use Psybeam!”
Also, Abra doesn’t learn Psybeam. Psychic could have worked because it’s a TM move, but Abra has to evolve to learn Psybeam.
Also, why is Winslow using two Pokemon when Vincent only has one? That’s seems unfair, especially since he’s a newbie trainer… I think.
That brings me to another point. I know nothing of Vincent. I don’t know his appearance, age, personality- nothing. Your description is lacking, too. It’s decent, I suppose. I can follow the battle fine, but it’s a fine line.
So: sparse up the description, give more character to Vincent, double-check which attacks Pokemon can learn, and then you should be good to go. :)