The case
Reruns of the modern Stone Age family ran all through the '70s and '80s, the vitamins were on every bathroom shelf, and still the first T disappears when people write the name.
The name is a pun on flint, the stone, which is why the second T exists. Said quickly, "Flint-stones" collapses to "Flin-stones," and the written version follows the spoken one.
Why our brains do this
Consonant clusters get simplified in speech, and spelling from speech drops the letter you don't pronounce.
Sources: Wikipedia — The Flintstones · Wikipedia — False memory: the Mandela effect
