The animation looks very nice and very realistic. And to top it all off Nathan generously shares the .blend file with us as well.
Find the links below after some more info from Nathan:
In my latest animation, the two main characters are candles. Naturally I needed a very nice flame to go along with them. I tried particles, which looked okay when the candle was stationary, but as soon as the candle moved around too much, the particles trailed behind. In addition, the particles were slowing down Blender, slowing down the render, and sometimes Blender would crash when I rendered an image with the particles. So I scrapped them and went a different way. I made a candle flame out of a mesh. It looks better than the particles did, it is much easier to control than the particles, and it renders much faster than particles.
The candle is controlled by a very simple two-bone armature. It's all procedural textures. Feel free to use the candle as it is or changed to suit your needs. But please credit me if you use it unchanged. Thanks.
An animation of the flame
(right click and save as please!)