I stumbled on this by a lucky accident. I find it very useful from time to time.
+ Flame is a very thin rectangular cube. OK to texture front and back.
+ Flame texture is a single PNG image of a flame (emission / transparent).
+ Flame mesh is animated with a single bone at its base (Armature modifier). "Preserve volume" must be on.
+ A Point lamp is also parented to the same bone, near the tail. It casts nice shadows, especially in Eevee.
+ Add some random noise to the bone: rotation X, scale Y, rotation Z. (With a modifier if you are lazy, or keyframe manually if you are ambitious.)
+ Play the animation and tweak all the parameters until it looks nice and realistic. It's handy to define the noise to make the animation loop seamlessly.
Very nice to learn the new trick! Thank you! I think that the method is probably similar to: https://www.youtube.com/watch?v=LPz42U54Wqg