Flickr does have an API for the site. If you can find a generic utility that will copy your Flickr collection to somewhere else, you can update your WP posts to lead to the new location by using one of the utilities meant for moving WP sites. The Flickr path/filename in the new repository should be maintained so the search and replace WP utility merely needs to change the staticflickr.com domains in your posts to the domain of where ever the images ended up.
PHP is a very capable language. A complete solution could be custom coded to do virtually anything you want. For example, find all posts with Flickr image references. For each reference, fetch the image, save it to the uploads folder and create a related attachment post (if Flickr Manager didn’t do so already). Update the post to reflect the new location.
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