"They're on Fire!"

"They're on Fire!",
Does this skill affect creatures that are already burning(ie.burning spirits)?
or does the affected creature need to be burned from the party(ie. SF).

Burning Spirits do not count. ToF requires the foe to have the burning condition (from any source: player spells, flame jets, other foes, etc). Burning Spirits, being fire based creatures, are immune to burning. The name is just a description.

This skill reduces damage taken from any target that is inflicted with the burning condition, regardless of the source of the application.

Burning Spirits or any other fire elemental or foe with a visual appearance of being on fire is irrelevant. The foe must be inflicted with the condition of burning, which is the sole requirement for fulfilling the condition of "They're on Fire!".