Thank you Simon ! 
Yes, it’s a camera oriented plane, here is a preview of my material for the fire :
Nothing very complicated here, I actually have only one noise and one mask, which are those :
I use a sphere mask to use the distorded mask as an input and get as a result, a nice gradient that I can directly input in the opacity. There is some artefacts created by the sphere mask on the base of the fire, I remove them with a simple multiplied gradient.
The wind is created by a vector to give the direction and a simple perlin noise to give more motion.
Hope this answered your questions ! Don’t hesitate if you have more 