When getting Rhodes out of the suit, there is a scene showing Killian breathing fire.
Why did he not use the same against Tony Stark when fighting him at the end of the movie? Or why did he not use it again at all?
Watching the scene again, it's quite clear the fire-breathing moment was the result of a purge required after sustained use of extremis' exothermic capabilities.
After applying extreme heat through his palms (for what is inferred to be some time), Rhodes is ejected from the suit. Killian seems to struggle for a few moments in an attempt to contain the sudden halt of this process, before venting the built up energy through his projectile fire-breath.
Both Killian and Savin look somewhat shocked at this. It appears as though this has never happened before, but perhaps only because circumstances have never dictated such application.
Killian even make a remark about this, claiming it is 'new day' in reference to this development.
Given the spontaneity of the reaction, its unlikely Killian would be able or willing to try and reproduce it in a weaponized way...
Let's take a few things in mind:
I remember Killian was asked what happens if you go too hot. Maybe he took a huge chance doing that and it was really close to the "too hot" point. That's why his accomplice looked so shocked that he would go to that extreme and take that chance. He definitely was glowing aloy brighter than the others usually did when using the power.