Fluid sims are just so darn fun! Nice writeup, very accessible.

Couple of notes, I think you forgot to apply timestep when adding rocket exhaust velocity, pretty sure it should be

  u[idx] += backward.x * flame_velocity_amount * falloff * delta
  v[idx] += backward.y * flame_velocity_amount * falloff * delta

You need to compensate by scaling up flame_velocity_amount, I used 85, seemed about the same.