The Homicidal Drunk Phase is not a Zoan form, it's what happens when Kaido taps in his inner Oni Race just like SeaKings get Red Eyes when they go into primal Rage Or Arlong's Pupils get thin and vertical like some cat..
And there's no such thing as Flaming Zoan form, Kaido is still in his base Zoan form inside the Magma Dragon..
Now Kaido didn't use Awakening in that fight, the reason is because he's an Oni race, he can't use Awakening or
he goes completely Berserk and lose conciousness like Pekoms when he goes Sulong..
But Kaido definitely has Awakening, he never use it though.. His Demon race makes him unable to use that power
efficiently.. Else he would be as strong as Prime Whitebeard..