Hello,
I'm currently messing with the pyro solver and when I change the turbulence, the smoke is affected but not the flame. Using 19.5.773.

Edit: I learned that in order to get turbulence on the flames, I needed to apply turbulence to the incoming particles that are upstream from the pyro source node

2nd edit: adding "flame" to the threshold field in disturbance, turbulence etc under the Shape tab in the pyro solver will affect the flame, if density is in the threshold field it'll be affecting the smoke. So if you want both the flame and smoke to be affected the threshold field will look like: density flame