AfriForum was on Friday denied leave to appeal Deputy Judge President Phineas Mojapelo's ruling that the gratuitous display of the apartheid-era flag amounts to hate speech.
The Nelson Mandela Foundation (NMF) and South African Human Rights Commission (SAHRC) took the case to court, asking that the gratuitous display of the flag be stopped.
The application seeking leave to appeal was heard in the Equality Court, sitting in the Gauteng High Court in Johannesburg on Friday.
Advocate Mark Oppenheimer, appearing for AfriForum, argued that there was a reasonable prospect of success that a different court will come to a different decision, based on a number of reasons, including the right to privacy.
He added the fact that the ruling was binding on all South Africans meant there was a compelling reason why the matter should be heard by a different court.
Advocate Ben Winks, for NMF, argued they did not believe that there was any reason another court would come to a different decision, but said leave to appeal should be granted if there were "compelling reasons".
One of the compelling reasons held was that the finding was not necessarily binding in provinces other than Gauteng, where the ruling was made. A declaratory order in terms of what constituted hate speech was needed, it was argued.
Mojapelo did not agree with either party, saying an order made by the court applied nationally.
The NMF agreed with the judge, saying it had been persuaded by Mojapelo's reasoning.
It argued, however, that the case was of national importance and should go on appeal.
The SAHRC's representative, advocate Itumeleng Phalane, said she would oppose the application for leave to appeal the court's decision.
More to follow.