Same "permission denied"
It appears as though Photo Mechanic is still using the old credentials. There may be a permissions issue with the file where the credentials are stored preventing you from overwriting the old data. I recommend that you check the modification date of the file below and make sure that it was updated when you last authorized Photo Mechanic in your Flickr account.
/Users/<your_name>/Library/Preferences/com.camerabits.PhotoMechanic/fileupload/templates/builtin/Flickr-conn.yml
If the modification date of the Flickr-conn.yml file is before you had reauthorized Photo Mechanic, then I recommend that you delete the Flickr-conn.yml file, empty the Trash, and authorized with your Flickr account once more.
HTH
-Jerry