How do you get the Burning Hunger Icon?
It was sold in the League of Legends store. Riot's description in the client reads: “This icon was released in the store for purchase during 2015 for the Zombie Slayer event.”
Is the Burning Hunger Icon still available?
Probably not. Riot tied the Burning Hunger Icon to 2015 (store purchase), and it does not normally bring back past event rewards or bundles.
