At the moment that Montag says this to Beatty,he is telling him that now, he was going to use the flame thrower to "Burn right," starting with him, getting rid of his captain was an act of passion and rage, a combination reaction to the burning of his own house.
Montag is happy to be free of the house, with its huge tv screens and the sick, unhappy life that he led there, he does not know that Mildred is not inside. He looks at this experience as a way of wiping out his old life, that which needed to be burned, purified. Therefore his statement to Captain Beatty is a way off informing him that he sees the value in the use of fire, now, he will use it to really get rid of what is poisoning his life.
As Beatty taunts Montag with memorized lines from Shakespeare, Montag's fury rises.
"Why don't you belch Shakespeare at me, you fumbling snob? There is not terror Cassius in your threates, for I am arm'd so strong in honesty that they pass me as an idle wind, which I respect not! How's that? Go ahead now, you second-hand litterateur, pull the trigger. He took one step toward Montag."
"Montag said, We never burned right..." (Bradbury)
Meaning, that now, in setting the Captain on fire, he was using the fire equipment for a sound and valid purpose, the right reason to burn, to purify and get rid of that which was poisoning the society, starting with Captain Beatty.
"He burns his own house and then turns his flamethrower on Captain Beatty, killing him. Montag then makes his escape from the city and finds the book people, who give him refuge from the firemen and Mechanical Hound that is searching for him."
The burning of his house and his Captain as well as the fire trucks symbolizes Montag's transformation from a mechanical drone who follows orders, to a thinking, feeling, emotional person, who has now broken the law and will be hunted as a criminal. He is an enemy of the state once he turns his back on the social order and burns his bridges, so to speak, he is set free, purified and must run for his life.