That would be an uncommon reading of the Fifth Amendment. Currently the Amendment has this to say:
No person shall be [...] deprived of life, liberty, or property, without due process of law;
Due process does not mean "terminate on sight, no questions asked, using any method of death that you can imagine in the rage of the battle." If the police is allowed to burn whoever they want, as long as they allege "bad things" done by the person, what stops them from stealing a page from the book of Count Dracula and impaling people in the courtyard of the police department? Even the Spanish Inquisition did not burn people without a trial (however formal it was.)
A conspiracy nut would be quick to say that nobody really knows for a fact that Chris Dorner wrote this manifesto or killed those people. Anyone could have written the document, and anyone could have killed the victims. Dorner would be then "advised" to disappear because he is a dead man walking. I personally don't think that this conspiracy theory holds water, but it is theoretically possible - and that's why we have lawyers and courts, to find out what actually happened.
Without that safety check you, an innocent person, can be easily framed for any crime - and executed on the spot by the arriving police. Someone standing over a dead body is *always* the killer, never a Good Samaritan, isn't it so?
As matter of the Constitution, nobody in this land can even "surrender his right to due process." There is no such mechanism in the Constitution, and for a very good reason. Otherwise a tyrant will always find leverage against the opponent (his children, for example, or torture) to make him surrender his rights.
It is true that the police is allowed to use force to stop a crime in progress. However, with Dorner holed up in the house, there was no crime in progress, there was no imminent harm to anyone. I'd use the situation to field-test many robots that are made for exactly these situations. Some robots can even navigate complex urban terrain, climb stairs, carry weapons. Send them in, control them from a safe location, and let them break the doors, investigate who is inside and where, deploy pepper spray and Tasers and non-incendiary tear gas, and in the end the criminal inside will be forced to surrender.
Dorner wouldn't have killed himself if he could get out of it alive simply because he'd want the trial as a platform from which he can further expose the LAPD. The act of burning him was either stupid (if done without thinking) or criminal (if done to silence Dorner forever.)
Firing at law enforcement officers in the execution of their duties is an automatic forfeiture of due process. If you shoot at me you are forfeiting your right to due process as I have a right to self defense.
Either way, why don't you go and find a 2nd Amendment protected and observant American and take a shot at him/her to test your theory... I'm fed up with hearing your #$%@ing shit!