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."
If you use it like a 301 we'll treat it as such.
— John ☆.o(≧▽≦)o.☆ (@JohnMu) May 10, 2018
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.
The HyperText Transfer Protocol (HTTP) 308 Permanent Redirect redirect status response code indicates that the resource requested has been definitively moved to the URL given by the Location headers. A browser redirects to this page and search engines update their links to the resource (in 'SEO-speak', it is said that the 'link-juice' is sent to the new URL).The request method and the body will not be altered, whereas 301 may incorrectly sometimes be changed to a GET method.
Forum discussion at Twitter.
Update on July 12, 2021, Google now made this official.
