A jury found him guilty after a high-profile trial in the High Court at Auckland and he was jailed for life.
Following a failed appeal in the Court of Appeal, Kempson then applied to the Supreme Court for leave to mount a fresh appeal against his murder conviction.
A decision was released today revealing Kempson's application had been dismissed entirely.
"In their verdict, the jury showed that they were sure that if the applicant did not intend to kill the deceased, he at least intended to inflict bodily injury which he knew was likely to result in death," today's ruling said.
"The most that could be taken from the applicant's account is that Ms Millane may have consented to the application of manual pressure to her neck for the purposes of sexual gratification.
"There is nothing in what the applicant told the police to suggest that she consented - or he believed she consented - to the infliction of bodily injury of a kind likely to kill her.
"For these reasons, albeit slightly differently expressed, the Court of Appeal was of the view the argument failed "as a matter of fact".
"We see no apparent error in this conclusion."
The court further explained its dismissal.
"The conclusion of both Courts is that consent does not, at least in the circumstances of this case, provide a defence to the intentional infliction of bodily injury known to be likely to result in death," the decision said.
"There is insufficient doubt as to that conclusion to warrant leave being granted.
"This is because it is difficult to see how a court could responsibly hold that consent is a defence to violence carried out with murderous intent."
It was also revealed Kempson faced two other trials last year for sexual violence against two women after the high-profile murder.
He was found guilty of all nine total charges at both trials, including rape, which he is now appealing against.