Lawyers for Jenkins, who was found guilty and sentenced to life imprisonment, claimed that the scientific tests usedwere flawed and unsafe.
Billie-Jo, 13, was bludgeoned with a heavy metal tent spike at her family home in Hastings, East Sussex, in 1997. At the trial, the prosecution case hinged on 150 microdots of her blood found on Jenkins's clothing.
The Crown claimed in the hearing at Lewes Crown Court that expert evidence proved the blood could only have been found on the person who delivered the blows. The prosecution said Billie-Jo would not have been alive 15 minutes later, when Jenkins said he found her, and a dying person's breath would not have produced that kind of blood spotting.
But Anthony Scrivener QC, representing Jenkins, 41, told the appeal: "This turns out to be inaccurate." He said evidence would be produced to show that the blood could indeed have been sprayed on Jenkins as he tried to help.
Mr Scrivener told the Lord Justice Kennedy, Mr Justice Dyson and Mr Justice Penry-Davy that there were 13 grounds of appeal, principally on the blood evidence and the judge's misdirection of the jury.
He said that, according to the prosecution, Jenkins would have had no more than three minutes to carry out the attack, in which at least nine blows were delivered, and then drive off with two of his four natural daughters on a trip to the local DIY store.
Mr Scrivener added that during the trial the defence legal team had agonised over whether to call evidence from two of the four natural daughters of Jenkins and his social worker wife Lois, which would have supported their case.
Some of that evidence was "highly significant", said Mr Scrivener. One daughter, Lottie, then nine, had referred to the side gate to the garden being closed when they drove off and open when they returned. Annie, who was 11, recollected speaking to Billie-Jo just before they left on the shopping trip. Neither girl heard raised voices or screams, and neither spoke of their father showing any anger towards Billie-Jo.
Mr Scrivener said the family had been worried about crime in the area, with 45 burglaries in their street in four years, including one at their home. Jenkins had no motive for killing Billie-Jo, there was no evidence of sexual molestation and she had settled to a normal life with the family in her four years in their home.
The judges agreed to hear the fresh evidence, despite objections from Crown counsel Camden Pratt QC that it would add nothing to what was said at the trial on whether Billie-Jo could have breathed out with enough force to produce a fine spray of blood. However, the judges indicated they would hear the witnesses before deciding whether to take the evidence into consideration.
The hearing continues.