Adopting your point of view results in finding that it is not unreasonable to equip the police with flamethrowers, and no violation of the 8th amendment could occur as long as use of the flamethrower was reserved for people not in custody. No constitutional violation of the 8th is possible, says you, until a person is in custody. Burning them is not punishment.
Or, if not flamethrower, just allow them to use gasoline and matches to burn houses that contain a person know to have committed a capital offense. It is quicker and cheaper process, that's for sure.
Second of all, a flamethrower is not a practical tactical weapon in such a situation. Flamethrower operators in WWII generally had very short lifespans.
I just don't see the problem of lethal force by arson versus lethal force by firearm here. They obviously had failed to shoot their way to ending the siege, as they couldn't see the perp. They hadn't been able to smoke him out with 'conventional' tear gas. Burning the cabin down ended the siege with no further loss of life to the LEOs on the scene.
I guess we'll just have to disagree as to whether it is a reasonable tactic. It certainly was viable.