His main team is Articuno, Yveltal, Decidueye, and Primal Kyogre. Right away, there's a clear Ice and Electric weakness that you can thwart. Oh, and, PK, if you're reading this, I love those Pokemon.
He leads with Yveltal and Articuno, using Reflect with Articuno and Tailwind with Yveltal. The obvious choice is to get a Tailwind user and take Articuno down before it sets up Reflect, hindering your ability to break through Primal Kyogre's mediocre defense.
So what's the first Pokemon I suggest? Whimsicott or Lunala. Whimsicott gets priority Tailwind to counter Yveltal's, or you could opt for Lunala if you prefer a Tailwind setter with an offensive presence. Both are good choices, but I would go for Lunala to take out Decidueye later in the match.
Now that you've countered Tailwind, you need something to outspeed Articuno's Reflect or even a Pokemon with Brick Break. So, what do you need? Something to knock out Articuno or something to Taunt it.
This is where my second choice comes in. To be honest, the team has a large weakness to physical electric types. So, while very, very uncommon, I would recommend a physical Tapu Koko. Here's why.
It gets a very fast Taunt.
It sets up Electric Terrain, boosting its electric moves even further.
It gets a super effective move for each of PK's Pokemon (Wild Charge for Articuno, Yveltal, and Primal Kyogre, and Brave Bird for Decidueye).
K, so PK refuses to give me the EVs for his Pokemon, so let's look at the calcs for what I think his EVs are. Starting with Articuno, PK claims it survived an Overheat from Primal Groudon in harsh sunlight. You can assume that this means it is fully invested in Special Defense and HP, leaving almost no room for Defense EVs.
4 SpA Groudon-Primal Overheat vs. 252 HP / 252+ SpD Articuno: 248-294 (64.5 - 76.5%) -- guaranteed 2HKO
So let's see.
252 Atk Life Orb Tapu Koko Wild Charge vs. 252 HP / 4 Def Articuno in Electric Terrain: 455-538 (118.4 - 140.1%) -- guaranteed OHKO
That's assuming that the 4 extra EVs aren't invested in Special Attack.
Next, Yveltal. I believe he runs 252 HP and 4 Defense so...
252 Atk Life Orb Tapu Koko Wild Charge vs. 252 HP / 4 Def Yveltal in Electric Terrain: 476-562 (104.3 - 123.2%) -- guaranteed OHKO
OK, so Articuno and Yveltal are down. Primal Kyogre is probably the toughest member of his team, I mean, that's a bit obvious, since that's why this question was asked :P
His Primal Kyogre I think has 252 SpA, 252 Spe, and 4 HP. Its main strategy is to outspeed with Tailwind, but hopefully Tailwind is shut down and instead you have it. Maybe it's 252 SpD though, I'm not 100% sure, but it doesn't really matter.
252 Atk Life Orb Tapu Koko Wild Charge vs. 4 HP / 0 Def Kyogre-Primal in Electric Terrain: 499-588 (145.9 - 171.9%) -- guaranteed OHKO
It didn't really stand a chance.
Now, for Decidueye, I recommend using Lunala. Tapu Koko probably killed itself via recoil unless you used Roost once, though you probably didn't have time to.
I believe his Decidueye runs 252 Atk, 252 Spe, and 4 HP with Jolly (though it may be Adamant).
252 SpA Lunala Moongeist Beam vs. 4 HP / 0 SpD Decidueye: 338-402 (113.4 - 134.8%) -- guaranteed OHKO
So, there you go, two good Pokemon to counter PK's entire team. Note that I guessed the EV spreads based on movesets he posted as well as the info he told me about his team.
Tapu Koko @ Life Orb
Ability: Electric Surge
EVs: 252 Atk / 4 SpD / 252 Spe
Jolly / Naive Nature
- Wild Charge
- Dazzling Gleam / Brave Bird
Lunala @ Lunalium Z
Ability: Shadow Shield
EVs: 252 SpA / 4 SpD / 252 Spe
IVs: 0 Atk
- Moongeist Beam
Hope this helps! :)