But it is solar powered. The sun shines on plants. The human eats plants (or, more indirectly, animals) to generate heat to power the flashlight. Of course, there are a lot of losses along the way so there isn't much energy left to power the LED.
Congrats to her for coming up with an interesting, if impractical, science project. There's a link in the article to a video of her describing her project and it shows that she considered how much power is available from a Seebeck/Peltier device, how much is needed to power an LED, and what voltage is needed to overcome the forward LED drop.
As an emergency power source, it might be better to mount the one surface of a Peltier device on a metal bar and heat the other end of the bar in the flame of a gas stove or a barbeque grill which would still work during a power outage. An enhanced temperature difference across the Peltier device could be achieved with a heat sink on the surface opposite the one touching the hot metal bar. Power from the device could be used to charge a battery for the flashlight. Or, instead of a flashlight, an LED on a stick might serve as an electronic candle for use during an extended power outage or for camping. The battery of the electronic candle could be charged using a stove, grill, or campfire during the daytime and then provide some light at night.
The project was likely a good learning experience for her. In the comments below the video, someone mentions that both her parents are engineers. I don't know if that's true but, if so, who can claim that we don't all stand on the shoulders of giants? She just happened to be closer to some shoulders than many of us.