Would the Skull Island be enough to feed King Kong?

It eats some epic monster for breakfast, then the next day it also kills some different epic monster.

This makes 365 epic monsters per year.

Epic monsters don't come out of thin air. They grow.

If island can sustain 365 epic monsters per year. It should also house thousands of gargantuan monsters. Then there would be hundreds of thousands of large monsters and also millions of normal sized monsters and tens of millions of normal animals non-monsters. Just to sustain the King Kong's consumption. What if there were 10 apes in family?

Maybe they grow in a few months or weeks (like in the Alien(s) movie)?

Answer

Kong isn't just eating food from the island, he's also gathering sustenance from the sea.

A squid partially emerged from the water. This was a true giant, far larger than any Chapman had ever seen or even heard of before, perhaps eighty feet from tip of tentacles to the end of its tail. It was a powerful creature. Several limbs remained hooked onto something beneath the surface as the ape tugged and wrestled to haul it out. Water churned in the violent struggle, turning dark as the squid released sprays of thick black ink that spattered down around and over Chapman. It stank, a heavy viscous fluid that stuck to his clothes as thick as tar.

...

Chapman curled against the rock and waited for it to all go away. He was moaning softly, listening to the sounds of the giant ape eating. The tentacle end lying across his legs went limp, then was jerked away as the beast finished its meal.

_{^{Kong: Skull Island - Official Novelisation}}

There's plenty of food in the ocean, enough to feed an entire army of giant apes.

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Additionally, as has been pointed out in comments, the island itself acts as an entry-point into an entire hollow-world ecosystem of giant monsters living under the Earth's surface.

Their hypothesis is proven correct but quickly draws the attention of Kong – which was the real motive behind the bombing of the island. The giant gorilla makes swift work of the helicopters that the scientists and their escort arrive in. Once they’re stranded in various parts of the isle, the scientific team and the soldiers work their way around the forests and jungles, encountering giant spiders, pterodactyl-like birds and massive water beasts – seeing first-hand the kind of life that exists around a hollow earth waypoint.

_{^{Screenrant: Skull Island: King Kong’s Backstory Explained}}