Someone here had a project where he designed a brass "lighter" that had a high powered red diode and was threaded for adjustable focus. It's probably still not too far down in the forum. We figured out though that even at 100mW or more, it would be really hard to get a flame going. My best suggestion was to make some char cloth, (like from a flint and steel kit) and use the laser to get it glowing, then transfer to the tinder. However, it would not be very dramatic.
I haven't heard much since. The main problem is that most burnable materials like wood, tinder etc. are "light" and will not absorb significant laser energy to ignite. The best you could probably do is light a red colored match head stuck in the tinder with a high powered green laser from a few feet.
But that begs the question, why not just use the match in the first place?
A better bet would be to create a "fire lighting effect". You will need a partner for this. Your scoutmaster might just think it's cool enough to help you.
Carefully arrange your fire pit with a model rocket igniter (The little match-head things on two wire leads) with some more matches and a good supply of properly arranged tinder and kindling a in the center of the logs. Have buried wires (cheap speaker wire is good, it's already got two wires in it.) running to an accomplice with a 9V or a 6V lantern battery. Just use a camp shovel to make a slit in the dirt running away from the fire pit for the wire, then step over it to conceal it.
Shine your laser into the fire into the center where the tinder is, and then have your buddy close the circuit on the igniter a few seconds later. If you have a bit of showmanship, a sense of timing, and your accomplice can keep a low profile, it should be a pretty awesome effect.
When I was in scouts, we had some "remote start" campfires where the leaders had prepped something like this. I don't know if it was electric, or if they just hid a long timed length of fuse, or a smoldering cigarette in the fire pit and lit it before we got there. They then had all the scouts gather around the fire, and say some bogus Indian "fire chant" louder and louder, and then they lit it. Nobody was fooled, but it was fun anyway.
With your laser, they would be fooled, at least until they were let in on the secret.