
Is that even something an individual can do, right out-from-under the author? I have no knowledge of these things; is the manuscript now the exclusive property of the publisher or is there still some aspect of it being Harry's intellectual property? It's possible this might actually come as a relief to him, if he's been trying to "walk it back" but the publishers won't let him.
It probably depends. They might have all the publishing rights to the book, but Harry would retain the rights as author. They might just have the first printing rights. If he's smart, he negotiated to retain and later sell the movie/tv rights. If he's not, then the publisher might have bought those too.
For example, L.J. Smith wrote the Vampire Diaries. Later, she sold the rights to make it into a TV show. When she did that, she also sold the rights to the characters so they could be developed by someone else. Later, when she wanted to write new stories for her version of the characters, she couldn't do it as the author. She had to do it as "fan fiction", since she no longer owned the rights to the characters.
Contrast that with a very savvy J.K. Rowling who may have sold some rights so her books could be turned in to a movie franchise and even a theme park, but she retained all rights to her work and was able to be very involved in the movies and even in the them park development.
So, it depends on what Harry signed.
Anyway, even if KC bought the rights, he'd have to buy the rights to the story to kill it or Harry could just write another memoire. Or leak the same info via another format, like a podcast. I think, without Harry's consent, KC buying up the rights could backfire. How do you buy the rights to a person's life story? Characters and fiction - yes, but his life is another thing. And if Harry did write another one which looked very much like the first, how would KC fight for the rights without revealing the contents of the first, buried memoire?