This widely watched video claims to be audio from the infamous Krakatoa explosion. Is it authentic?
No, it's not authentic.
Simon Winchester discusses in depth the explosion in his book "Krakatoa: The Day the World Exploded, August 27, 1883", and there are absolutely no records of any form of equipment recording audio — much less video.
Could there have happened to be some kind of gramophone nearby that happened to be recording and happened to capture some oblique aspects fo the sound? Possibly, but highly unlikely.
The technology was only 5 years old in 1883 — and exceptionally expensive still.
Indonesia also wasn't exactly a hub for new technology in the 1880s — the latest tech known to be in the country was the telegraph (itself a 40-year-old invention, but that only had been in-country for a few years as part of the Reuters news service (per Winchester's book)).