For a pretty extensive discussion of the subject, see http://www.thefiringline.com/forums/...d.php?t=379063
 If you actually do shoot at someone, or even draw your gun in self defense, running away is a very bad idea. You will want to be the first person to report the event to the police. Running equates to guilt. If you run, you'll have a very tough time selling the proposition that you were justifiably defending yourself.
And let's say someone presented a lethal threat, you drew your gun; and he ran away. There's a possibility that he'll run to a phone, call the police and report that "some nut up the street just drew a gun on me." Now the police are looking for you, and you might have an uphill fight convincing them that you drew your gun in legitimate self defense.
You will be better off if you are the first to report an incident. The first to call tends to have the most credibility.
 As to the right to remain silent, the nature of a self defense claim is that you will have to tell your story. It's something of a question of where and when, but being the first to report the incident helps establish your credibility and your bona fides as the "good guy."
Ordinarily, in a criminal prosecution the state must prove the elements of the criminal offense beyond a reasonable doubt. So if the crime charged, and for which the defendant is on trial, is, for example, manslaughter, the state must in general prove to the jury beyond a reasonable doubt that (1) the defendant was there; (2) the defendant shot the decedent; and (3) the defendant intended to shoot the decedent. The burden of proof falls solely on the prosecution, so the defendant's strategy is to say nothing and put the prosecution to its proof; or attack the prosecutions evidence to create a reasonable doubt; or try to cast doubt on the state's claim that he was there (alibi defense), that he pulled the trigger (some other dude done it), or that he intended to shoot the decedent (the gun went off by accident).
But all of that is completely inapplicable when the defendant pleads self defense. If the defendant claims self defense, the prosecution doesn't have to prove, at all, that the defendant was there, that he shot the decedent or that he intended to shoot the decedent, because the defendant will have admitted each of those elements of the crime of manslaughter. If the defendant is claiming self defense he necessarily must admit that he (1) was there; (2) shot the decedent; and (3) intended to shoot the decedent.
If you are claiming self defense you will have the burden of producing evidence that your conduct met all the elements needed to satisfy the applicable legal standard for justification. Only once you have done so does the prosecutor now have the burden of proving that the defendant's actions were not justified. And even though you may not have the burden of proving justification, the less convincing your evidence is, the easier it will be for the prosecutor to disprove justification.
The principal evidence supporting your self defense claim will be your testimony. You will need to testify, and that means you will be subjecting yourself to cross-examination.
How difficult it will be for the prosecutor to successfully attack your self defense claim will in part depend on how convincing your story is, and how strong the evidence supporting your story is. Things that could, in the minds of your jurors, damage your credibility will be bad for you (and things that enhance your credibility will be good for you). Not having promptly reported the incident or having left the scene equates to guilt and may irredeemably damage your credibility.
 If you shoot someone in self defense, stay, get out your cell phone, call 911 and tell them that you have just been attacked and defended yourself. Ask for police and an ambulance. And then you wait.
When the police arrive, basically what Massad Ayoob, Marty Hayes, Kathy Jackson and others recommend is:
* Say something like, "That person, or those people, attacked me." You are thus immediately planting the notion that you were the victim.
* Say something like, "I will sign a complaint." That establishes that you viewed the conduct of the other party to be criminal. It also shows a spirit of cooperation.
* Point out possible evidence, especially evidence that may not be immediate apparent. So if the assailant's knife slide under a car, tell the investigating officer. If the assailant dropped his gun in the bushes as he ran away, mention that. You don't want any such evidence to be missed.
* Point out possible witnesses.
* Then say something like, "Officer, you know how serious this is. I'm not going to say anything more right now. You'll have my full cooperation in 24 hours, after I've talked with my lawyer."
 Take a class from Massad Ayoob and/or read Kathy Jackson's and Mark Walter's book, Lessons from Armed America
. Doing so will be very helpful in dealing with these kinds of questions.