King Kong is a kaiju-scale ape — Batman's gadgets aren't designed for building-sized opponents.
MonsterVerse Kong is hundreds of feet tall. Batman's utility belt is designed for human-scale threats. While Batman has access to larger vehicles and weapons through the Batcave, his standard loadout doesn't include kaiju-fighting equipment.
With prep and access to Justice League resources, Batman could potentially develop anti-Kong countermeasures. But in a standard encounter, he's a man in a suit against a creature the size of a skyscraper.
Batman with prep and vehicles could theoretically fight Kong — the Batwing has serious firepower. His tactical mind could exploit Kong's intelligence (which is high but not genius-level).
Kong is hundreds of feet tall, weighs thousands of tons, and has primate intelligence with tool use. One casual hand swipe ends Batman entirely. The size gap makes standard Batman equipment irrelevant.
Kong wins in any standard scenario. Batman would need serious preparation and military-grade hardware to even be in this fight.
Batman also fights
King Kong also fights