Does magic damage from Gromp debuff proc spell vamp
The Cinderhulk/Bami's Cinder/Sunfire Cape aura does not proc spellvamp or any other on-magic-damage proc except for the healing reduction of morellomonicon. However since it deals magic damage it will benefit from magic penetration.
The Gift of the Toadstool (Gromp buff) works a bit differently. It will apply all magic damage effects (Spellvamp/Liandry's/Rylai's) and it counts as Poison which means a cassiopeia will gain passive stacks and a cooldown reduction of her E against a target that's poisoned with the debuff.