I have the Coolpix 2200 with an SD card, but maybe the answer is the same.
I first have to hit the "Play" button wich lets me see the pictures I've taken. Then when I hit the "Menu" button, I get options including "Delete" (selected images), "Delete All" (requires confirmation, i.e. ""Sure?"), etc. Without first hitting the "Play" button, I don't think I can get to the "Delete All" command.