Under current law, the orders of a police officer are to be obeyed at all times. Failure to comply is a crime. So is attempting to flee an officer. As is resisting arrest. But as public scrutiny of fatal shootings that stem from the commission of these crimes increases, don't be surprised if efforts are made to undermine the legal standing of commands by police.
The idea of "right to flee" or "right to resist" may already have legal precedent. The Massachusetts State Supreme Court last year threw out a man's felony weapons conviction because it found that police didn't have probable cause to chase after him when he ran away as officers tried to question him about an unrelated robbery. In their ruling, the justices even went so far as to write that African-Americans in Boston should be allowed to flee police--due to the department's record of racial profiling.
There have also been cases where defendants have successfully argued that they had a right to fight back against arresting officers due to a fear that they themselves would beaten. A number of police departments have adopted policies that they will not engage suspects in high speed pursuits--hoping that they can later identify and apprehend those criminals in less-dangerous situations. The cumulative effect of these decisions is that efforts to evade or resist arrest are given legitimacy--making modern policing even more difficult.
We may be forced to ask ourselves some very difficult questions as a society: Is a situation that threatens "just" the life of a police officer justification for his or her use of deadly force? Should criminal suspects be given legal avenues of escape? Should arrest just be a voluntary thing? And should police be disarmed like their counterparts in Europe--where officers are forced to fight bomb and gun-toting terrorists and criminals armed only with batons?
Personally, I prefer a society where the legitimate commands of an officer hold the force of law. I want police to make every effort to take criminal suspects into custody as quickly as possible by whatever legal means are necessary. And I want officers to be able to defend themselves with deadly force if they have identified a real threat to their personal safety. In the meantime, all of us can make sure we stay out of situations where law enforcement needs to be arresting us.