When you make any changes to a photo that is included in a set that has been published to Flickr it moves from the "Published Photos" section to the "Modified Photos to Republish" section. When the set is published these are supposed to update the existing image on Flickr (as per this page: How to publish photos from Photoshop Lightroom Classic CC to Adobe Stock and social media), but Lightroom just re-uploads it, creating a duplicate on Flickr (albeit with the updated version of the image). I have just updated to the latest version of LR Classic, 7.2, to no avail.
It isn't explicit, but under the heading "Upload to Flickr", part 2, it says "If prompted, click Replace to update published photos with newer versions", which clearly implies that photos which are being re-published should replace their existing counterparts on Flickr rather than being added again.
However, I think you're right about the Pro account level requirement. This is not well-documented on Flickr's end, and you can replace photos on a free account via the website which is why I thought this should be working, but the API does appear to restrict this to Pro accounts; error code 1 for the photo replacement API is "Not a Pro account": https://www.flickr.com/services/api/replace.api.html
I have now started to get this issue. I have a Pro account and have been able to update images with no issues but I am now getting dupes every time I republish. I don't think it started right after the Mojave upgrade but I do't recall it before wither. Anyone have any thoughts as I am at a standstill ATM.
Additional - I have just been back to take look at some earlier uploads and it was happening before the Mojave update. It seems that any image that is updated creates a new version.
I am getting the photos to be republished in Flickr. There are 55 photos I have not touched in years. I have a pro account and contacted them, they said it was a bug in adobe. I talked to adobe tech support they told tme to edit settings then leave as is. so this is the second time in a couple months, I am running the current version of Lightroom classic and Windows did an update right before this happened.