Strange, because I always remember Flickr having horrible UX. You could never just open an image file directly; if you tried, Flickr would always redirect you to a page which obscured the image behind an invisible layer which obscured pointer events such as right-click.
I learned quickly to avoid Flickr links.
I believe that is to prevent hotlinking, which isn't the purpose of the service.
Maybe it was like that for a while? But flickr allowed image downloads, there was a dropdown in the UI with the available sizes for years. And it had an API (+stable URLs) to download images.
It's possible they did not allow the way you tried to access images directly, to enable control of the downloads for the photographer. But I think you misjudged the behaviour back then, they were pretty open.