In order to delete a kit, you'll want to go to the kit page, and look for the "Edit This Kit" button that appears in the right margin of the page. Click that button, and you will get a pop-up. “Delete This Kit” appears in the lower left corner. 

Have a look at the screenshots below. See "Edit This Kit" on the right side of the image?

Select “Delete This Kit” in the lower left corner: