If a face-up "Fire King" monster you control is destroyed by a card effect (except during the Damage Step): You can Special Summon this card from your hand. During the next Standby Phase after this card was destroyed by a card effect and sent to the Graveyard: Add 1 "Fire King" card from your Deck to your hand, except "Fire King Avatar Barong".
Special summons when your Fire King monsters are destroyed by card effects, which happens when Fire King Island is used.
Searches for another Fire King monster if it's destroyed by a card effect.
Search effect happens on your next standby phase.
Needs a face-up Fire King monster to be destroyed by a card effect to special summon Barong. This means you can't use Fire King Island to destroy a Fire King monster from your hand to special summon it.
Fire King deck often uses Sacred Phoenix of Nephthys, and uses Fire King Island to special summon it easily. This often involves a lot of card effect destruction, including your own monster(s) when your field gets destroyed. Through its effect, you can destroy a Fire King monster you control to special summon Barong and search for a Yaksha.
Since the Fire King play style revolves around monsters getting destroyed and sent to the graveyard, you can use Powerful Rebirth to bring back your monster. This lets you use Fire King Island's effect on your monster again to either special summon a Fire King monster from your hand, or as a searcher. It also still works well if you use Sacred Phoenix of Nephthys since the monster summoned by Powerful Rebirth will not get destroyed when the trap card is removed from the field.
Adds from Deck to hand
Special Summons itself from your hand
I like this card on the phoenix deck, it makes it much faster. However, after the Abyss Box, Phoenix is quite irrelevant.
But there are strong cards from her archetype that have not been released yet.