Really.
Please show laws that proscribe the manner of deadly force (gun, nightstick, etc.)
You are raising an absurd standard.
I think you meant "prescribe," which is to list what is allowed. "Proscribe" is a prohibition. Not meaning to nitpick or attempt to put you in a bad light. Maybe you just made a typo, but mixing "prescribe" and "proscribe" is not uncommon.
As far as means of deadly force that are forbidden, I submit the eighth amendment. I submit that "burning" is a form of cruel and unusual punishment, under US law. Plus, burning is a fairly slow way to disable an attacker, and unless trapped in a building, is an unreliable way to prevent escape. Firearms, bow and arrow, spear, sword, hammer, axe, baseball bat, and other devices deliver more immediate results.
I think the burden is on the police, if they do admit resorting to arson, to justify that resort.