"We are working with the Royal Household to consider how flag flying policy can be applied in changing circumstances, such as when a member of the Royal Family steps back from public duties".
Speaking to BBC News NI, Councillor Carl Whyte said flying the flag would be an "immoral position".
It is not clear how this impacts on Northern Ireland.
The royal family reputation is in peril right now between Prince Andrew's scandal and Prince Harry and Meghan abruptly stepping away from their royal duties.
Breckland District Council were approached for comment but did not respond.
"The reason he stepped down was due to his relationship with Jeffrey Epstein but that is not the reason we will not fly a flag".
Mr Rodgers said his was a view shared by his party.
Prince Andrew stepped down from his royal duties in November after a disastrous BBC interview in which he failed to express regret for his friendship with Epstein and offered a slew of weird claims to defend himself against allegations that he had sex with Virginia Roberts Giuffre when she was 17.
An Assembly spokeswoman said: "The Assembly Commission has agreed that Parliament Buildings flies flags on the designated days determined by the Department of Digital, Culture, Media and Sport (DCMS)".
Flying flags on government buildings in his honour "would be wholly inappropriate", opposition Labour legislator Wes Streeting told The Sun daily.
The Duke of York has asked to defer a military promotion to Admiral after stepping down from public duties in the wake of the Jeffrey Epstein scandal, Buckingham Palace has confirmed.
A Buckingham Palace spokesperson said the Duke had asked to stall the promotion until he is able to fully resume royal duties.
But there was a public outcry after the prince gave a BBC interview last November, where he failed to explain adequately why he did not cut off ties with his friend earlier than he did, or to express much empathy with Epstein's alleged victims.
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"The bells are rung for the birthdays of HM the Queen and HRH the Duke of Edinburgh and their children", a spokeswoman said.