"In an emergency, a crayon will burn for 30 minutes."
Ok. I'm trying to get through this post without laughing. For some reason this image alone makes me laugh every single time I look at it. I also thought I would try something different and do a video post for this bad idea. Because honestly, this is a REALLY bad idea.
So lets get down to why you shouldn't do this. On youtube I found just a few videos of people attempting this. As I showed in the video, I did one crayon with your basic lighter, and another with my work torch. I actually seemed to have had better luck with my lighter than I had previously seen on other youtube videos, but the torch, due to its higher temperature and more focused flame, got the job done quicker. My theory on why this works is that it's like a reversed candle - the paper on the outside of the crayon acts as a wick, and the melting wax inside the crayon helps coat and protect the paper from just going straight up into flames.
But they don't burn for 30 minutes. Maybe 10-15 if you're lucky. In my video I show how at the 5 minute mark it's already halfway burned though. Also, the image above has it sitting on someone's carpet. Which is just remarkable as far as "really bad ideas" go -- not only are you faced with dripping wax on your carpet, most carpets are made with synthetic fibers and when they catch fire, it's not good. The wax itself is just a simple paraffin wax, which is commonly used in candles and even foods, but this experiment caused a lot of smoke to form, leaving my studio smelling my melted crayons for quite some time.
All in all, this is just not a good idea. The crayon itself isn't stable, making it very prone to tipping or falling over, it doesn't last long, and it puts off a lot of smoke. I can't think how this would ever be a good idea. In a pinch you're better off even making a homemade oil burning lamp with olive oil than you would this. But the majority of people generally keep candles, lanterns, and flashlights on hand in case of power outage.