KiCAD allows you to create non-plated through holes (NPTH), otherwise known as mechanical holes. There's one wrinkle: when generating drill gerbers, two separate files get generated, one for the plated holes and one for the non-plated holes. There does not seem to be an option in KiCAD to change this.

The solution is simple. Open up the layers in gerbviewer (gerbv), which you are surely already doing. Select only the two drill files as active, then go to File → Export → Excellon drill Merge..., and save the file as your YourName.drl file (overwriting the original.)

To confirm that it has worked, reload the .drl file in gerbviewer, and note your holes have appeared. Remove the NPTH.drl file from the list. Zip everything up, upload to kicad, and confirm your holes are there, et voila!