I'm having the same symptom mentioned in this thread: http://forums.adobe.com/thread/1058075
In the Flickr Publish service configuration dialog, the Authorize button pops up a dialog that explains "Lightroom needs your permission to upload images to Flickr," but when I click that dialog's Authorize button, it appears to do nothing (no browser, no error message, etc.).
I am currently running Windows 8 Pro 64-bit and Lightroom 4.3 64-bit.
Here's a history of this problem.
I was using Windows Vista 64-bit with an updated Lightroom 3 (version 3.6?). I was publishing to Flickr using the built-in Flickr publish plugin. That worked flawlessly for the last year, and I never had a problem.
I then upgraded to Windows 8 Pro 64-bit. Unfortunately, I did not test Lightroom 3 at this point.
I then upgraded to Lightroom 4.3 64-bit.
After these upgrades, I tried to publish two photos to Flickr using my existing Flickr publish configuration. I believe that I got some error the first time, which I did not write down. I wasn't sure that the Flickr publish service would upgade correctly, and I did some searching online.
I'm familiar with the Flickr APIs, and I thought that after the upgrade, I probably needed to re-authorize the plug-in. I went to my Flickr account in my browser and revoked Lightroom's permissions. I may have also clicked "Remove Authorization" in the Flickr publish plugin's settings page. After that, I started hitting the problem described above. When I click the Authorize button, I never get a browser pop up.
I then tried a few things.
Between each of those steps, I rebooted the machine. When the machine came back up, I opened Lightroom 4 and clicked the Flickr publish service's "Set up" button. I then when to the plugin manager and reloaded the Flickr plugin. Finally, I clicked "Authorize" in the Flickr plugin's settings. Every time, I get the same behavior. "Not authorized" in the settings dialog changes to "Authorizing..." while it shows me a dialog. I click the Authorize button in that dialog. I briefly see a different message in Flickr publish service settings page (Waiting for response...). Then it changes to "Not Authorized." I never see a browser or an error.
With each experiment, I tried with both IE and Firefox set as my default browser. I get the same behavior with both browsers.
I verified that running "start lightroom://www.flickr.com" from the Windows command prompt opens Lightroom 4.3. Therefore, I believe that the registry settings for the lightroom URL protocol are correct.
I have never used the Facebook publish service in the past, but I cilcked on the set up button for that plugin. When I click Authorize on Facebook, it launches my browser (or opens a new tab) for Facebook. Therefore, it looks like Lightroom plugins are able to launch the browser.
It seems like there's something wrong with the Flickr publish service plug-in itself. I'm not sure how to get any additional diagnostic information from the plugin. I'd be happy to try something else, but at this point, I'm out of ideas for troubleshooting.
I can try switching to Friedl's Flickr plugin, but I'd rather just see the builtin plugin fixed or my current problem diagnosed.
I worked with Gokul from Adobe support, and we eventually stumbled into the solution.
The system clock was wrong!
Based on something Friedl says on the blog for his Flickr plugin, the Flickr authentication APIs will fail if the system clock is wrong. His plugin helpfully points out that the clock is wrong when you install it. It also reports the error that he gets from the Flickr APIs: HTTP 401 (not authorized). Unfortunately, Lightroom's builtin Flickr publishing plugin doesn't report any error, and it just fails silently.
In my case, Windows appeared to be displaying the correct time, but the time zone was incorrect, and my system time was actually 3 hours ahead. I reset the clock and timezone and restarted Lightroom. Now, the builtin Flickr publish plugin is working again.