As of March 2020, the "Watch on Prime Video" link takes you to the 1996 animated series, not the '50s live action series. However, at least the first episode of the animated series isn't bad, and it features Paul Shaffer (former Saturday Night Live and David Letterman music director) as Dr. Zarkov!
Review of Flash Gordon
Flash Gordon
(1954–1955)
2020-03-18: "Watch on Prime Video" link is not for this series
17 March 2020