Yes — replacing the actual image on Flickr from Lightroom should work, including with Flickr plugins such as jf Flickr, and it is usually very fast/near-immediate once the publish succeeds.

Key gotchas from the reports:

• You must republish from the Flickr publish service/photostream or photoset, not just edit locally.
• If Lightroom prompts to Replace/Update, confirm it.
• “Mark to republish” may not force an upload unless Lightroom detects a real image change.
• If syncing fails, re-authorizing the Flickr service/plugin may help; one user also reported changing the default browser helped during authorization.
• Make sure Lightroom is up to date.

A simple workflow is: publish the image, make an actual edit, return to the Flickr publish service, select the photo, click Publish again, and accept Replace/Update if prompted.

If you don’t see the change, the most likely causes are that no real image change was detected, the publish was done from the wrong queue/location, or the Flickr authorization/plugin connection needs refreshing.