Hey there! To be specific but not longwinded, the NES had 5 audio channels that could make noise at any given time. There were two pulse channels (most leads), a triangle channel (most bass), a DPCM channel (for samples for crude voice, or drums etc) and lastly a Noise channel.
The 'burn' sound is a sweep through the available sounds within the noise channel. This was a very common thing back in the day, and I used it myself when creating some of the music you'll hear in Null Divide+
As for battletoads~ It's an amazing tech demo for the nes, but a pretty rough game. It's apparently unbeatable in 2player mode, as one of the levels instantly kills player two at the start each time. They just didn't test it.