Not much of an artist, but I think I can help you a bit.
What screen alignment are you using? It looks strange in your last image.
Your colors look a bit off, the fire looks too red at the end. Fire colors are easy with a BlackBody node. Use a Color Over Life or Dynamic module to set a temperature, and feed Particle Color or Dynamic Parameter into a BlackBody node in your material, multiply with a monochrome flame texture and feed into emissive.
I made this modifying the blackbody particle system in Content Examples/Effects. The initial particle is like a liquid, it carries momentum, falls due to gravity, and doesn’t grow or spread much. Dying spawns a more flame-like particle with Event Generator and Event Receiver modules. It inherits velocity but has high drag. It grows, spreads and cools rapidly, and accelerates upward. A collision event spawns a similar particle that starts hotter, grows, spreads and rises faster.