File:Hell's Angels by Hunter S. Thompson (1967 1st ed jacket cover).jpg

English: Scan via Christie's. Cropped by uploader.

English: Published by Random House. Jacket design by Joseph del Gaudio. According to Gonzo.org, Thompson himself took the photo used for the cover, though this is uncredited on the jacket itself.

English: No permission is required because the dust jacket was first published prior to 1978 without a valid copyright notice. Hell's Angels was first published in book form in 1967. The book itself had a valid notice on the copyright page and its contents were previously published in The Nation, 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.

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."

If just one of these elements is omitted, the work is deemed to be published without notice and is not eligible for copyright protection. Neither the year "1973" nor a copyright symbol (or any acceptable variant) appear anywhere on the dust jacket. The mere identification of the publisher, author, and jacket designer do not meet these requirements. The lack of notice on the dust jacket can be verified by examining full-jacket scans at this AbeBooks listing or this one.