Apologies for the inconvenience - please follow the instructions below based on your OS:
With rekordbox closed, could you please open the Finder and click Go > Go to Folder... from the menu bar. Enter this in the pop-open window:
Inside you'll find the file SoundCloudSetting.txt - please delete that file.
Press Command + Shift + . (dot) and hidden files will be shown; delete the .soundcloud folder.
You can press Command + Shift + . (dot) again to hide the hidden files again, then launch rekordbox and login to SoundCloud again.
If that does not work, use the same technique as above to go to this folder:
...and provide a copy of the SoundCloud.log file as an attachment to your reply.
With rekordbox closed, open the following folder:
C:\Users\<yourusername>\AppData\Roaming\Pioneer\rekordbox6 -- note that the AppData folder is hidden; enable hidden files in the Explorer preferences.
Delete the SoundCloud folder and the SoundCloudSettings.txt file, launch rekordbox, try logging in to SoundCloud again. If you still have problems, please provide the following file: