You will run into some folks who say that capitalizing pokemon nouns when you're not strictly using them as proper nouns is a crime against the English language, but I think it's safe to ignore them. The reality is that this is fanfiction for a franchise that uses idiosyncratic capitalization in all of its official media. You're not obliged to "correct" the style of the source material, no more than you would be to correct Homestuck's spelling, grammar, and capitalization in a spin-off story.
That said, you're not obliged to adhere to every facet of the source material either, and that includes leeway to change its code of style to more resemble regular literature. As Bay and Astinus have said, the most important thing is to be consistent. You can decide to make an exception of just about any rule as long as you fully understand the rule itself and why you're making an exception.
Personally, I pick a capitalization scheme on a fic-by-fic basis. Sometimes I want it to sound like a more direct video-game adaptation, other times I want something that's more grounded. Sometimes I'm working with a universe where people refer to a pokemon collectively as a species in the singular. (Not "charmander are short and wolves are strong," or "Charmander are short and wolves are strong," but "Charmander is short and Wolf is strong.") This I think is both similar to how Pokedex entries are written and makes sense for spiritual cultures.
One more thought, here's why I think the official media capitalizes words all over the place: if you don't know what you're reading, "seel," "onix," "dewgong," etc. are confusing and just make it look like the writer can't spell. The capitalization is easy shorthand to convey that these are invented, Pokemon-specific terms and not the Queen's English. I've also found that even though I'm pretty knowledgeable about Pokemon, the capitalization helps in fics I'm reading helps when there's a 4th or 7th gen pokemon that I don't recognize. It becomes, "Oh, that's a Pokemon," instead of, "What's this gibberish?"
tl;dr: Keep Calm and Be Consistent