No permission is required.

1. First, the photo is a mechanical scan/photocopy of the original cover and does not qualify for independent copyright protection.
2. Second, the dust jacket was first published prior to 1978 without a valid copyright notice. Cat's Cradle was first published in 1963; the hardcover book itself carried a copyright notice, so its contents remain copyrighted. However, the first-edition dust jacket did not carry a separate copyright notice. According to The Compendium of U.S. Copyright Office Practices: Chapter 2200, § 2207.1(C) at p. 15:

"A notice of copyright on the dust jacket of a book is not an acceptable notice for the book, because the dust jacket is not permanently attached to the book. Likewise, a notice appearing in a book is not an acceptable notice for the dust jacket or any material appearing on that dust jacket, even if the book refers to the jacket or material appearing on the jacket."

The jacket's lack of a copyright notice is self-verifying; someone looking to double-check can examine the image itself, which can also be found on Commons here.

Keep in mind that the pre-1989 requirements for copyright notice were highly formalistic and, other than a few enumerated exceptions, required these three elements:

1. "The symbol © or the word 'Copyright' or the abbreviation 'Copr.' or an acceptable variant such as "(c)";
2. "The year of first publication for the work"; and
3. "The name of the copyright owner, or an abbreviation by which the name can be recognized, or a generally known alternative designation of the owner."