If I use Team Rocket Nidoking ex's "Tainted Horn" attack and the Defending Pokemon is already Burned, would I also put 8 damage counters for the Burned condition?
No, the text of Tainted Horn is only referring to the Poisoned condition.
Tainted Horn





×2

Tainted HornYour opponent's Active Pokémon is now Poisoned. During Pokémon Checkup, put 8 damage counters on that Pokémon instead of 1.



Kingly ImpactPokémon ex rule
When your Pokémon ex is Knocked Out, your opponent takes 2 Prize cards.
If I use Team Rocket Nidoking ex's "Tainted Horn" attack and the Defending Pokemon is already Burned, would I also put 8 damage counters for the Burned condition?
No, the text of Tainted Horn is only referring to the Poisoned condition.