In his appeal to the 5th U.S. Circuit Court of Appeals, Haynes, who is black, contended State District Court Judge Jim Wallace improperly allowed Harris County prosecutors to exclude two black people from consideration as jurors. The ruling violated Haynes' right to a jury process free from racial discrimination, his attorneys argued.
The U.S. Supreme Court, in a landmark 1986 ruling, found it unconstitutional to dismiss a juror because of race.
Prosecutors contended two of the jurors were stricken from consideration because of their demeanor, but the appeals court said Wallace, who upheld the juror removals, wasn't even present during the individual questioning of the jurors.
The jury that convicted and then condemned him included one black person. Of six potential black jurors interviewed during the selection process, four were stricken by prosecutors. One was eliminated by Haynes' lawyers.
The 5th Circuit opinion, posted late Wednesday, said a second judge was presiding during the individual questioning while Wallace was on the bench while the jury pool was questioned as a group. There was no explanation for Wallace's absence.
The juror claim was among several raised by Haynes in his appeal to the New Orleans-based court. All the other claims, however, were rejected.
The ruling gives Haynes what's known as a certificate of appealability, which allows him to move forward with his appeal.
Haynes, now 29, was arrested two days after Kincaid's death.
The 40-year-old officer was off duty, riding with his wife, when the windshield of their car was hit by what authorities later determined was a .25-caliber bullet fired from a passing truck. Kincaid followed the truck and pulled up alongside in northwest Harris County.
When he got out, said he was an officer and reached behind to get out his identification, he was shot in the head. Kincaid, a 13-year officer, was not armed at the time of the shooting.