The island kingdom destroyed in J.R.R. Tolkien’s Second Age history is Númenor.
Númenor was an island realm in the Great Sea, given to the Edain after the War of Wrath at the end of the First Age. Its people, the Númenóreans, received long life and great knowledge, but they were forbidden to sail west to the Undying Lands. Over generations, fear of death and resentment of the ban grew among many of the kings.
The downfall came under Ar-Pharazôn, who challenged Sauron and later tried to invade Aman. In Tolkien’s mythology, Eru Ilúvatar changed the world and destroyed Númenor, while the faithful survivors escaped to Middle-earth and founded Arnor and Gondor.
Númenor is sometimes compared with Atlantis because both are legendary island civilizations destroyed by catastrophe. Tolkien’s account, however, has its own theology, chronology, peoples, and connection to the history of the Dúnedain.