The Original
The Blaze takes his name partly from his appearance and partly from his use of smoke and fire in crime. He attempts to organize Gotham criminals under his control, and as the Baron Von Peltz lures Batman into a trap.
The Second
Citizens of Gotham are having buttons stolen from their clothes. It seems a small thing, especially since one person only lost one, another two, and another three. But then the button-victims are each found dead in some sort of fire. Batman investigates and finds the first victim was a rich man, the second a poor man, the third a beggar. Someone is apparently stealing their buttons as trophies prior to killing them in the order of the old nursery rhyme. It’s a person in a fireproof suit, who calls himself The Blaze. Further investigation finds all the victims were once members of a suburban volunteer fire company. The Blaze is unmasked as the fire-scarred Jim Garth, the father of someone who died in a fire the volunteers were unable to put out and who irrationally blames them. When confronted by Batman and Robin, the Blaze runs into a cave and seemingly dies when the cave collapses in on itself.