"Or Kurt Vonnegut, who famously advised against their use" is in the article

If you read the article linked in the comment, they say Vonnegut was, probably, kidding about the semicolons.

Who probably also advised to never listen to advice from successful authors.

It isn't clear whether his advice here is just humor. This article goes on to explain that he uses semicolons in his own work, even in places where he didn't need to.

It might be part humourous, part the type of advice that is good for those that don't know when to break it.

It's easy to over-use semicolons, and you often see people who have just discovered them use them all over the place for no good reason.