I just realized that I wrote a verbose version of L.Dutch's answer. I upvoted his answer. You should, too.
It's amazing how often I've used the following quote on this site....
Can you launch an ICBM horizontally?
Sure. Why would you want to? (The Hunt for Red October)
Can you shave a piece of wood so small that it could be used for a campfire by an ant-sized human? Sure! Why would you do it?
Here's the problem: rate of combustion. It doesn't matter if you're burning wood or oil or anything else. The simple truth is that the smaller the combustible item is (i.e., the less you have of it), the faster it will be consumed.
As in... fractions of a second.
I'm fond of another quote by Harold Ramis about the original Ghostbusters. During the scene when the giant Stay Puft Marshmallow Man is walking down the street, kicking over (among other things) fire hydrants, the special effects experts used very finely ground sand for water. Why? He explained...
You can't miniaturize water.
It's true. You can see every time a movie puts a model of something (like a ship) in water for filming. The water is the wrong size. It's motions out of proportion with the object of our focus. It can't be miniaturized.
Neither can chemical reactions.
And that's the problem. Yes, they could have a campfire. For a fraction of a second. If they added fuel fast enough to keep the reaction going, they'd burn themselves up (or ignite whatever was around them).
So, from a practical perspective, no... ants can't have campfires.
But that shouldn't stop you. This stack is dedicated to building imaginary worlds that need not conform to Real World physics. If you want your ant-sized humans to have campfires, let them have campfires. It's not as if there's a secret cabal of fanatic bibliophiles out there ready to unleash their zombie hordes when they discover (gasp!) that you've written a story that doesn't conform to real-world physics.
P.S., it's worth noting that there may be some chemical compound that could ignite easily and burn slowly enough that mere grains could be used by the ants as a campfire. Such a combination of chemicals won't be available just anywhere, suggesting that they can't be used as a campfire, so I ignored that possibility. But that could, itself, be an interesting idea for a story. Is there a compound that is easy to ignite and yet mere grains could burn for a specified time (you'd need to specify that)? Hmm...