As a side tip, it's probably going to be better to actually go back and rewrite the story. While, yeah, your writing style changed since then, because this is a sequel, you might be drawing on something that isn't even explained in flashbacks.
Think of it like this: take whatever sequel to a movie you can think of. (Most anime movies don't count because they tend to draw off the series instead of the movie before it and are therefore made for the fans anyway. Pokémon's a case-in-point there.) Because I don't know your tastes, I can't really offer a specific you might know, but for my sake, I'm just going to go with
Men In Black II as an example. In it, you've got a secret government organization that defends the world against aliens. Easy enough to get. What you might not get so easily is why one of the main characters started off in a post office with no memories of ever actually being in the organization. While the movie tells the audience how he got there, there's still a sense that they're missing something -- like a view of how that character got to be so formidable and why exactly he decided to get a memory wipe in the first movie. There's still elements that, no matter how much the sequel tries to explain, can only really be understood if someone watched the first one.
Same thing goes with sequels to fics. While you could have flashbacks, you just can't get everything in the first fic to show through in the second. There might be things that the reader will feel would be better understood if they saw everything in chronological order -- that is, by reading the first book with all of the events in the right order, rather than brought up whenever you need to explain something.
That and an overuse of flashbacks tend to be jarring unless it's for narrative purposes anyway. (For example, Dragonfree's "Curse" makes heavy use of flashbacks, but the timeline's supposed to be twisted to begin with.) If you're trying to tell a more linear story -- where the flashbacks are only necessary in explaining things instead of to create a convoluted timeline and where the story is actually supposed to move forward through time instead of back and forth -- then you'll end up with a more jerky feel, if you catch my drift. As in, it'll be a little like suddenly throwing a car in reverse at semi-random intervals. Not exactly a smooth ride.
Not to mention if you're writing a sequel, chances are, you'll want to be satisfied with the first book because you're using it as a foundation. Going back through, making corrections, generally updating it, and posting it here will not only give us a chance to read what the fic is following but also allow you to polish the first book to your liking. It's not really unheard-of to go back and do some editing on a previously published work. Lots of fic authors do it all the time, even if their fics happen to be long as all mess.
Other than that, to answer your question, fanfiction communities generally don't really care what you do for the sake of inspiration. If it'll help you to go back and play through your game, go right ahead.
If you mean to ask whether or not you're allowed to basically rip dialogue out of the game and use it in your fic, that depends on how it's executed. If you use the dialogue but remember to go above and beyond and add something of your own creativity, it's fine to use the game. (
Example of a fan-created work that did this and pulled it off.) However, you should note that it's very hard to do, and you
do have to put a lot of work into making your fic have a little something extra -- as in, something that lets the reader know that they're not just reading Pokémon Emerald: Text Version. Readers tend to get bored with just reading through something they've already played through, you know?
Of course, since you
did mention you included changes (like a leaning towards battle descriptions), I'm not necessarily saying right off the bat that you don't know this. I'm just saying it for the sake of general advice.
Good luck either way.
