Google can treat 308 redirects the same as they treat 301 redirects, says Google’s John Mueller. That is, of course, if you actually do redirect the URL to another. John Mueller of Google said on Twitter “If you use it [a 308 redirect] like a 301 we’ll treat it as such.”

Google Drive uses a 308 redirect as a Resume Incomplete response to indicate to the client when an incomplete upload stalled. So that is a bit different. But you can use it as a normal redirect.

Forum discussion at Twitter.

Update on July 12, 2021, Google now made this official.