Create a Flint - Then use it in the inventory by clicking on the RMB

Yes, I did that. 10 times for creating the flint
almost 50 times the RMB while right next to a placed campfire.

at least, the UNLIT campfire.

For those who may come to this post in the future - I had the same issue as MKoR. The problem I was having was that I had "dropped" the campfire - not "placed" it. To place the campfire, right click it from within your inventory. If the campfire graphic is the same on the ground as it is when it is in your inventory, it is not lightable. The graphic will change if you "place" it. Then, right click the flint and tinder near the campfire. The flint and tinder is created by combining the mined flint with small rocks - you can see this recipe in the recipe window - open the recipe window by hitting the TAB key).

Unfortunately, the developer's effort to help didn't account for the difference between dropping and placing the campfire.

Also, it would have helped TREMENDOUSLY if the game gave the feedback "nothing to light on fire. your flint was NOT USED UP."

Consuming resources when performing an action that is utterly useless is an easy way to confuse casual users. But still, thanks for posting the info. I hope it helps someone...
It was also entirely unobvious how to place that campfire...