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To help answer your question, you can also think about what happens to a fire when you scale it up. This thought experiment will help guide you on whether the scaling is linear, or by volume (cubed) or perhaps even more dramatic than that. In the case of fire, if you imagine a campfire that is 10x the width, 10x the height, and 10x the depth, you are probably looking at a fire that has not 10x the energy, but more like 1000x the energy. It's got a massive energy output compared to a modest campfire, it is going to consume a lot more than 10x as much fuel, and it's potentially going to set stuff on fire and consume it and keep trying to consume more fuel in a way that you wouldn't expect a 10x sized campfire to, and it is a huge emergency that is difficult to put out for that reason. It's not just a 10x bigger fire because you scaled it up in 3 dimensions. It's a vastly bigger monster.
So vice versa, if you're scaling your body from roughly 1.8 meters to 1.8 milllimeters, that's a 1000x reduction, so you might want to take your campfire down to 1/1000th of its human-sized dimensions too. But you're probably not looking at a fire that scales down to 1/1000th with you, you'll be looking at a fire that only has 1/1000th-cubed or 1 billionth as much energy. That is a very small amount of energy, it will barely do anything or even be noticeable at that scale. It may not even sustain a flame. And if you want a campfire with more proportional energy like 1/1000th of a regular campfire for your ant-sized campfire, that means you'll need a campfire that is still 1/10th the physical dimensions of your human-sized campfire. So it's still a really, really big fire relative to your ant-sized body. It's maybe the size of a large candle or alcohol burner, but that's HUGE compared to ant-size dimensions. So no, put quite simply, it doesn't scale like that.
These estimations are approximate and there are probably even more complex scaling factors at play for something as physically complex as fire at such extreme scales, but that should help give you the general idea. You'd probably need much more thorough study and experimentation to get a better idea, unless somebody has already scientifically researched this which wouldn't surprise me.
Excellent answer.
On a side note: if I could get my ant colony to build small camp fires we could create some ugly forest fires, or some nasty building fires in large cities.