However, a Flickr discussion about Base58 encoded URLs exists from April 2009: https://www.flickr.com/groups/api/discuss/72157616713786392/
Did Flickr deploy their Base58 encoded URLs before the Bitcoin white paper was published on Oct 31, 2008?
I wrote that code, registered the flic.kr short URLs, and helped draft the initial OAuth spec to facilitate posting photos from Flickr to Twitter (having worked at both Obvious, Twitter's parent company, and Flickr)
It's _possible_ though extremely unlikely that I had read the Bitcoin whitepaper. However the Bitcoin addressing scheme isn't explicitly referenced in the whitepaper, and looking at my bookmarks, it looks like Bitcoin wasn't really on my radar until 2011. (I'd encountered PoW systems with hashcash and freenet, earlier, but that's orthogonal to this conversation)
The inspiration, as far as I can tell was the logic we put into generation gift codes as part of our 2006 launch of "Give the Gift of Flickr" -- which probably means it was George Oates idea, who was the lead Flickr designer and master of all things UX.
For anything more definitive you'd have to find someone who had access to the old Flickr SVN repo.