Time usually remains static in Pokemon games (Apart from the occasional Day/ Night feature), so why are we hurtled forward a year once we've finished? Surely you can just access the next region once you've completed the first.
Most towns/ cities are a lot more than just 2-3 houses. Only Pallete Town has less than five buildings, and have you seen the size of Saffron or Celadon?
It was basically a copy+paste. This is how the original opening to FRLG progressed: Get Pokemon > Battle rival > Get Package > Return to Lab > Get Pokedex and Pokeballs. You just added an extra two trainer battles between the rival battle and getting the package.
I would advise swapping the Eevee - You wouldn't be overpowered in the beginning and the Luck Charm could add another dimension to the story.
Can you say why Gold and Kris are at the lab? Are they there for a specific reason, collecting their starter Pokemon or just bumming around?
By 'Team Rocket's Rising', do you mean that you will be in the same time period as when Team Rocket got its act together and became a fully-fledged interational crime syndicate, or will there be a document/ NPCs talking about it somewhere in the story? If it is the first scenarion, you can't really include Gold, Kris or Silver because they wouldn't have even been born yet if you're going by Team Rocket canon.
I'm not really sure about the Rockets, Aqua and Magma all coming together to preform the 'take over the world' scenario. Magma and Aqua hate each others guts, so co-operating would be the last thing they'd want to do. Factor in the prime motivations for each team (Rockets: They want power, but not neccessarily enough to rule the world with an iron fist [This can generally be boiled down to a desire for financial power] - Aqua: Expand the seas at the cost of the land - Magma: Expand the land at the cost of the seas) and you can see that there is little to no common ground between the teams on a motivational level at least.
I have no problems with trying to keep your story somewhat secret, but most of what you put up earlier was not enough for me to adequately evaluate your story.