I've played with FireSteel (aka Swedish Fire Lighter to some people) and while making sparks is easy, making anything burn with them is actually pretty hard. You have to get the sparks to fall in the right place, and you need to have a reasonable understanding of how to make a fire in the first place. My experience of Scouts/Girl Guides are that most kids don't have that ;-) it's not how they make it look on TV.
Related to that, making a useful fire out of paper is going to be very hard. Yes, a sheet is easy to light, but it's consumed pretty quickly and then what. You can't hold a match to a phone book/ream of paper and ta-da, you have a burning torch to wave in the face of the enemy. Yes, you can get a nice fire going in a paper bin say, with a little patience, but is burning down the room the intention here? Making a cook-fire is different to making the sort of flaming brand they wave around on tv.
Also be wary of "lenses make fire!" it's not always true. Piggy's glasses in Lord of the Flies were divergent lenses (he was nearsighted), they wouldn't have worked.
If you want self-defence, is your nine-year-old the sort that might be stupid/clued-up-enough to use a
lighter and aerosol? Sounds like they're in a store room, lots of plausible aerosols to choose from (spray polish, air freshener, air-dusters for IT, etc). Of course, this relies on the kid having a cigarette lighter, thereby negating your original question. (PS, be sure to stop spraying before the flame reaches the can, or Bad Things happen...)