This is probably a stupid question but for the life of me I can't find it.
I've done a search and can't find it.
I've done a duplicate file search in delete mode and I have my duplicate files found and checked. Now, how do I delete all the checked files?
When you open the Duplicate Files utility window, just below the 'Search' button there is a 'Delete' button 
. If for some reason however you navigate away from the 'Duplicate Files' collection after the search is done and the results are shown - going BACK to the dupe files collection will no longer show the checkmarks, and the 'Delete' button will then be greyed out.