Solution #1

If you are trying to delete a system file, or a file from a protected system folder, then Duplicate Cleaner may block this.

To allow the deletion you can un-check the following option from the drop-down menu (top of main window).
Options->Protect important system files/folders

You should only delete these type of files if you know what you are doing.
 
Solution #2
If you get access or permission errors then be sure that you have the appropriate permissions to delete a file - this may apply if you are trying to delete system files, or files created by a different user.

Try running Duplicate Cleaner as administrator. You can right click on the Duplicate Cleaner icon and select "Run as Administrator".