Swamps specifically said they're "battery powered":
They're little low-powered LED lights, used in place of candles.
I'd also note that vegetable oil has a pretty high flash point, and is hard to light- except that ole' fur-covered Swamps is basically a walking wick. It'd be hard to get the puddle on the floor lit, even intentionally, but yeah, oil-soaked fox fur would probably go up like a stack of loose newspapers.
Let's just say there's very little danger from the lights, and there's several fire extinguishers over in the corner, out of the way.