Yes, I can make a rainbow one.
I have to say though, if I used the amount of particles I used in my screening of the flame, but in rainbow, it looks a bit faded. (30 emit amount)
http://i.imgur.com/oUHpiws.png

If I bump up the particles to 50 emit amount, it actually looks properly rainbowey.
http://i.imgur.com/sQh3oaM.png