There are two different mechanical hounds seen in this part of the book. We know that one of them is destroyed by fire, and we assume that the other one is as well, but we don't know for sure.
The first hound is the one from Montag's fire station. After Montag kills Captain Beatty with his flamethrower outside Montag's house, the hound attacks him. The hound does not fully inject its poison into Montag so Montag is able to destroy it. He incinerates it with his flamethrower.
Later, another hound is brought to hunt Montag. He escapes it by jumping in the river and then later by drinking the liquid that Granger gives him to disguise his scent. The hound goes back to the city and kills someone else so that the government can say that they caught Montag. That hound presumably gets destroyed when the city is bombed.
So, both hounds presumably burn. Montag gets the first one and the other one is destroyed by the bombing.