When this card is Summoned: You can banish 1 "Ninja" or "Ninjitsu Art" card from your Graveyard to target 1 Set card your opponent controls; reveal that Set card, then return it to either the top or bottom of the Deck. Your opponent cannot activate the targeted card in response to this effect's activation. You can only use the effect of "Red Dragon Ninja" once per turn.
Use Fire King Island's second effect before doing a normal summon. It can special summon Red Dragon Ninja from your hand if you don't have a monster in the field since it's a Winged Beast-Type monster. You can also use its first effect to send Ninja Monster from your hand, which Red Dragon Ninja can be used to activate its effect.
By using Hazy Flame Sphynx' effect along with Mai's Aroma Strategy, you can correctly declare the card type at the top of your deck. By doing this, you can Special Summon Red Dragon Ninja from your Hand or Graveyard since it's a FIRE monster.
Reveals face-down cards / Returns from your opponent's field to your opponent's Deck
Banishes from Graveyard for cost
Prevents activation of your opponent's Effect Monsters / Prevents activation of your opponent's Spell Cards / Prevents activation of your opponent's Trap Cards / Prevents responding to its activation