What all is considered "Spell Damage" to proc the 2%-4% burn DoT? Is there a general rule of thumb?
General rule of thumb? Anything
or spell vamp works on.
Other general rule of thumb? Anything that doesn't apply life-steal is considered a spell, with 1 main exception:
All on-hit effects that don't belong to
.
On-hit effects generally don't apply on-hit effects, with those 3 exceptions.
Otherwise - Abilities that are AA rests, AA steroids, or "apply on-hit effects" will essentially apply life-steal and not spell-hit effects.
On-hit effect abilities won't apply additional on-hit effects.
And then abilities (regardless of damage type - be it physical, magical, or true) will apply spell-hit effects like Spell Vamp, Rylie's, and Torment.
Some summoner spells even count towards this - Smite in particular has been used to make the plays with Olaf's spell vamp.
Second: Is Kayle's Divine Blessing [E] (empowered auto attack that also has magic damage and splash damage) considered to proc this passive because it causes "Spell Damage"?
Yup, that applies it. Kayle's one of the 3 special champions that gets an on-hit effect skill that applies other on-hit effects.
For her and Cho, I'm pretty sure they're coded more where every time they attack, a swag ability is cast at the same time.