This is the scent of dead skin on a linoleum floor
I'll get back to this. >_>
I was fighting but I just feel too tired to be fighting
In reference to tournaments, this could mean that this character was frequently placing, not necessarily well, but a lot. Or that they were placing somewhat, but now the character never places at all. Could also be a reference to the character's history in their games, if they decided to stop fighting.
Will we make a mark, this time
Could mean make a mark on the tournament scene, and combined with the previous line, means that the character is starting to gain use in tournaments after previously placing lowly/non-existantly. Can indicate potential.
I can't stop itching at the thoughts of tarnished hope
The character had some sort of tech or potential use, but that is now ruined either by the fact that it doesn't work properly/as it was intended, or it is not as useful as was thought. May also mean that the character seemed to have lots of potential ("hope") but was later found out it doesn't (which would definitely mean its Ike. Maybe)
We never talk of our lacking relationships
No one talks about this character's...lacking relationships? This is probably about the character's background, not their Brawl counterpart.
Every drop of flame lights a candle in memory of the one who lived inside my skin
I LOVE THIS LINE. This line is the thing that will tell us who the character is! The line means that the character has an "alter-ego" of sorts that used to live in his body. In other words, it is the past version of this character. In other other words, most likely, this character was in Melee! "Every drop of flame lights a candle in memory" indicates that the previous skin inhabitor was praised for whatever reason.
In other words, its Mario, Fox, Peach, or Jiggly, focusing only on the last line. It can't be Luigi or Ness because neither of them had incredibly significant changes made to them from Melee. It CAN be Mario because it could be a reference to Dr. Mario, who people always whine about for not being in Brawl (and thus praise him). Fox Peach and Jiggs were all nerfed from Melee, and thus, they are inhabiting the skin of their once glorious alter-egos.
I'll narrow this down even further in a bit.