1) "Calm down."
A person who is on fire will not be calm, but reminding them of this fact will simply upset them further. No matter how annoyingly panicked they may seem, you do not want to anger them. Instead, try to engage them in conversation. Although they'll just want to talk about themselves and the "extreme pain they're in" try to be a good friend and indulge their self-absorption.
A note here: try to refrain from yawning. People on fire can get quite offended if they suspect they are boring you.
2) "Smile More."
A burning person does not like to be told what to do, especially when it comes to facial expressions. Although when a person is ignited, a smile suits them much better than that eyes wide, mouth open, weird look of terror that is super annoying to look at, your concern may be construed as criticism. And that's the last thing they need.
A note here: telling someone to smile never, ever induces a smile that is genuine. And a fake smile is the worst, especially on someone who is in flames. Nothing says "I have lost my mind, and now I will haunt your nightmares" like a fake smile and a face on fire.
3) "Is it just me, or is it getting hot in here?"
Yes, it is hellishly hot, because you are standing next to a blazing heat source, but drawing attention to this will just embarrass the person on fire. And nothing stokes a fire like embarrassment, except maybe flammable gasses or chemical accelerants. If the heat is really bothering you, take a step back, and raise your voice. A person on fire's vision is blurred, so they won't be able to tell that you've stepped away.
Like most times in life, as long as you appear sensitive to a person's needs, even if they are the furthest thing from your mind, that's really all that matters.
4) "Whoops-a-daisy. Someone's clumsy."
The last thing someone on fire wants to hear is that they made a mistake. Believe me, they know they did. Say something more encouraging like "you'll get the hang of that burner eventually," or "I bet that's the last time you'll try dolman sleeves" or "Don't worry, the flames surrounding your whole body emitting this 1200 degree Fahrenheit heat aren't even noticeable." How about "You look thinner. Along with several layers of flesh, have you lost weight?" A little flattery goes a long way with someone who is burning.
5) "You will not believe what happened at Stacy's party. Do you have an hour? This is a long story and you're definitely going to want to sit down and get comfortable."
Stacy's party was interesting, no doubt about it, but people on fire tend to be self-centered. The fact that they're on fire is pretty much all they want to talk about it. Although you may feel like, "I get it. You're burning. Big deal." to them, it is a big deal. And even though you are dying to tell someone about Stacy getting super drunk at her party and cheating on Kevin with two different guys, you shouldn't waste juicy gossip on someone who is too on fire to care. Telling a person on fire anything of importance is pointless, because they simply refuse to listen. Instead, they will insist on interrupting you to beg for some water or a fire extinguisher.
Remember, do not take this personally. Allow them their limelight moment of screaming and attention-grabbing. Your moment will come soon enough.
6) "You look tired."
No one ever wants to hear that they look tired, and a person on fire is no exception. Even if their eyes are super-glassy and they are yawning/screaming incessantly and incapable of forming full sentences, that doesn't mean they can't still take offense. Instead, try to suggest they take a break. Advise them that sitting, lying down, or rolling on the floor is a good way to release some tension, so they can appear more rested and less agonized.
And, if worse comes to worse, just walk away and let them cool off.