Firstly the basic procedural line for the "tail" of the flame

After that the body / core of the flame

Another procedural shape to smooth the bottom edge of the flame

Some math to mix all masks and properties to handle every aspect of the silhouette

Added a grayscale noise texture to distort the silhouette

Reorganized the graph to isolate the offsets from the "distortion math"

Added just a scrolling offset to both of the noise blocks trying to preview the expected motion

Simplified the math removing useless redundant expressions and stacked 3 sucessive distortion samples scrolling at different offset speeds

Added another falloff to handle the tiling of just one side of the UV, creating a more "wobbly" tail by the edge of the mesh

Added an erosion effect by the end of the graph making use of the same distortion map, however, to "dissolve" the edges of the silhouette

Added transparency and color with an outer glow parameter to handle the "contours" of the flame

Added another falloff parameter to control the height of the flame that becomes dark smoke and another block just to pump it's color brightness to work with HDR and post processing

Mixed the distortion map to add and subtract from flame silhouette, removing the noticeable sharp blend between flame and smoke and creating the illusion of micro flames oscilating near the core of the flame