Building on from Fresh's answer, it is very true that Fire types cannot be burnt by a flame orb, and it's also true that all Pokemon that get Flash Fire are Fire types. However, say for instance that I was playing with some hacked Pokemon or balanced hackmons or whatever, and I gave a non Fire type Flash Fire. After an experiment I have just done, I can very safely say that Flash Fire does not prevent a non Fire type from being burnt by a flame orb
I hope this helps you in your future endeavors.
Experiment: http://replay.pokemonshowdown.com/balancedhackmons-311455441
