I found FAlbum (hat tip Geoffrey), which is

a Wordpress plugin that allows you to display your Flickr photos and photosets on your site.

[fa:p:id=1470804297,j=l,s=m,l=p]

It is NEARLY perfect. Key things that it is possible to do, but it cannot (as far as I can tell):
Add Comment, Add Tag, Search, Ordering of results. There might be more, but I think the addition of those features would make this a perfect app for displaying Flickr albums on a self hosted site.

I do think the dynamic displaying hook is neat. For instance, this is how I displayed this image
[ fa:p:id=1470804297,j=l,s=m,m=p], without a space after the first bracket.

First the impressions of this plugin, I’m very impressed. It’s what I’ve been looking for.