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Kougyoku (紅玉,Kougyoku?) formerly known as The Flame Emperor (炎帝,Entei?) is a companion and contracted beast of Touya on his journey. She is one of the Four Divine Beasts and also the leader of the Bird Beast.
Kougyoku's true form is a bright red bird as big as a horse which resembles a phoenix. She intuitively changed her appearance in a similar way to the Kohaku's form.
Kougyoku has a calm and gentle demeanor. She is shown as a perceptive creature as she intuitively guessed Touya's ability based on how he already got Kohaku and Kokuyou and Sango and she changes her appearance accordingly before being told to do so.
The Flame Emperor (炎帝,Entei?) which later known as, Kougyoku, is one of the divine beasts that can manifest in the world once every few decades or centuries unless she is summoned by a human. 
Intimidation Aura: She is able to release suppressing aura that renders all individuals, which have lower magic levels in respect to the divine beast, becomes immobile.
Long-Ranged Telepathic Communication: She is able to make telepathic communication with their master and among the divine beasts regardless the distance. They also able to include other people into this communication line.
Form Transformation: She is able to change her menacing true form appearance into cute young beast form (Child Form) and back as she pleased.
According to the character introduction, although based on her appearance, she looks flashy, she actually has collected personality.