Better to dimple rather than countersink. I assume you want the flush rivets to be smooth on the inside of the box.
You need a bench vice, a 2x4, #10 drill bit, male die set, place the male die in the hole you drilled in the 2x4 which is clamped in the vice.
You need something that you can hold the female die against the work piece while you hit & form the dimple with a hammer, (possibly the striker rod from your C-channel)
Probably some extra hands would help to stabilize everything.
Now you are set up for your 2 minute task! Dimple away