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Sadly, no. Touch of Flames requires its own standard action rather than being usable in place of any normal attack. As such, you can only use it on your turn, and only as a separate standard action. Never as an AoO, not with spring attack, nor on a charge.
If this is a home game you can ask if you DM will let you use it in place of a melee attack. It's not exactly a powerful attack, because it's a touch attack you cannot increase its damage with power attack, and since it's not a weapon you cannot enchant it either. The main draw of the ability is the free Flaming property, which it sounds like you would never get to use properly.
EDIT: Unarmed strikes are normally not considered an armed attack. This means you don't threaten with it and thus can't take AoOs with it, nor can you flank with it. If you have improved unarmed strike then they change to be an armed attack, like having a weapon on you and in hand at all times. Touch of Flames is not something you're armed with because you have to use it on your turn as a standard action, so you don't threaten with it either. If it were a spell you would be able to activate it on your turn, forfeit the attack and use it to threaten by using the "Holding the Charge" rules (and thus take an AoO or use it in place of a melee attack on your next turn). But it's (Su), so you cannot.