can a prosecutor mention that the defendant is not present during closing bc he is running from the law?

Flight is relevant evidence of consciousness of guilt. If you have presented evidence that the defendant has fled, you should be allowed to draw reasonable deductions from that evidence. If the defendant is on bond and failed to appear for closings, I would ask the judge to take judicial notice of the fact that the defendant was out on bond, and that he failed to appear at the scheduled time. That should be enough evidence to argue to the jury that he has fled.

under what authority

Many courts now allow you to simply cite postings on this Forum as authority.

Here is some stuff from westlaw:
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Cawley v. State, 166 Tex.Crim. 37, 40, 310 S.W.2d 340, 342 (Tex.Crim.App.1957)

When unexplained, flight has long been deemed indicative of a consciousness of guilt. "The wicked flee when no man pursueth * * *." Proverbs 28:1.

[2] Evidence of flight is admissible where one is charged with an offense, on the ground, in substance, that it is some evidence of guilt, and amounts in effect to a quasi admission of guilt of the offense charged. Damron v. State, 58 Tex.Cr.R. 255, 125 S.W. 396.

[3] [4] Escape, flight and attempts to escape are always admissible as evidence of guilt. Wilkerson v. State, 60 Tex.Cr.R. 388, 131 S.W. 1108, 1111.

See also:

RULE 401. DEFINITION OF "RELEVANT EVIDENCE"
"Relevant evidence" means evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence.

RULE 402. RELEVANT EVIDENCE GENERALLY ADMISSIBLE; IRRELEVANT EVIDENCE INADMISSIBLE
All relevant evidence is admissible, except as otherwise provided by Constitution, by statute, by these rules, or by other rules prescribed pursuant to statutory authority. Evidence which is not relevant is inadmissible.

Have you put on evidence before the jury about where defendant is and why?

I suppose it would be important to mention that he is on the run, AT LEAST IN PART, because of the instant charges. If he is on the run only because of some other extraneous offense then it might could be a problem.

We once started trial the morning after seating a jury. The defendant failed to show, so after an hour of waiting, the judge told me to begin my opening statement. I had a great time pointing at the empty chair next to defense counsel. The defendant showed up a couple hours later.

It was a very quick verdict.