I included Queens too, hope you don't mind :P
Arceus - Literally god of Pokémon
Aegislash - "Generations of kings were attended by these Pokémon, which used their spectral power to manipulate and control people and Pokémon."
Calyrex - "Calyrex is known in legend as a king that ruled over Galar in ancient times. It has the power to cause hearts to mend and plants to spring forth."
Spectrier/Glastrier - Calyrex's steeds
Serperior - Based on French royalty, the Regal Pokemon
Zoroark - King N's ace
Politoed - "The curled hair on Politoed’s head is proof of its status as a king. It is said that the longer and more curled the hair, the more respect this Pokémon earns from its peers."
Vespiquen - Has "queen" in it's name and is the queen of the Combee colony
Eternal Flower Floette - AZ's Floette
Tyrantrum - "A single bite of Tyrantrum’s massive jaws will demolish a car. This Pokémon was the king of the ancient world."
Slowking - King of intelligence. "Slowking can solve any problem presented to it, but no one can understand a thing Slowking says."
Nidoking - King of battle. "Nidoking prides itself on its strength. It’s forceful and spirited in battle, making use of its thick tail and diamond-crushing horn."
Nidoqueen - Has "queen" in her name
Tsareena - It's signature ability is "Queenly Majesty" and a Tsar (Tsareena) is an emperor of Russia
Jynx - "In certain parts of Galar, Jynx was once feared and worshiped as the Queen of Ice."
Rayquaza - As you said, "King of the skies" (and king of competitive)
Groudon - King of the earth
Kyogre - King of the sea
Palkia - King of space
Dialga - King of time
Giratina - King of the Distortion World
Reshiram - Queen of fire and truth
Zekrom - King of electricity and ideals
Kyurem - King of ice and emptiness
Xerneas - King of life
Yveltal - King of death
Zygarde - King of balance and the ecosystem
The Tapus - Guardian deities of Alola's islands
Solgaleo - King/Emissary of the sun
Lunala - Queen/Emissary of the moon
Zacian - "Able to cut down anything with a single strike, it became known as the Fairy King’s Sword, and it inspired awe in friend and foe alike."
Zamazenta - "Its ability to deflect any attack led to it being known as the Fighting Master’s Shield. It was feared and respected by all."
Aggron - "Long ago, there was a king who wore a helmet meant to resemble the head of an Aggron. He was trying to channel the Pokémon’s strength."
