Fellow councillor and Albury RSL sub-branch president Graham Docksey berated Cr Cohn after she supported the city funding flag poles to display the Aboriginal and Torres Strait Islander flags at Monument Hill.

The Vietnam War veteran said Cr Cohn had "tried to make" the RSL have an Acknowledgement of Country at Anzac Day services without success.

"Now she's trying to make us have the Aboriginal flag, it's a vendetta against the RSL and the veterans' community, forcing us to put a flag up that we don't need," Mr Docksey said.

"She's never acknowledged the Aboriginal plaque we put up there (at the memorial to mark Indigenous service personnel).

"She's never worn a uniform, she would never understand."

Cr Cohn did not respond on Tuesday to Mr Docksey's claims when they were put to her by The Border Mail.

Mr Docksey argues the Indigenous flags should not be flown at the memorial, alongside Australian and New Zealand ensigns because they did not exist at the time of World War I.

He says there is unanimous support for his stance among Albury RSL sub-branch members.

"They're 100 per cent against it, because they all have the same opinion that we all served and fought under the Australian flag," Mr Docksey said.

"If you're going to put an extra two flags there, why not have all the flags from the other countries that we fought with in World War I?"

Wiradjuri leader Liz Heta was reluctant to comment on the matter, saying she saw arguments for and against the flying of the Indigenous flags at the monument.

"I don't want to offend anyone," Mrs Heta said on Tuesday.

Mrs Heta noted the RSL had installed a plaque to specifically salute Indigenous soldiers and "there was a lot of negotiation around that".

That recognition was part of a $1.35 million upgrade, which was officially opened last month.

The existing Australian and New Zealand flag poles were shifted to be closer to the monument as part of that revamp.

At Monday night's council meeting, Cr Cohn moved that funding for two more masts at the memorial be included in next year's council budget as part of motion on a draft flag protocol.

The Greens party councillor said there was a community expectation that Aboriginal and Torres Strait Islander flags were flown at prominent civic sites, including Monument Hill.

Mr Docksey declared a conflict of interest before the debate on Monday night, but remained in the council chamber and voted against the motion.

He now wants those upset at the prospect of the Indigenous flags flying at the monument to put their concerns formally to the council as part of feedback on the draft protocol.

"I encourage everyone individually to put submissions in with fact, not with Greens policy rubbish behind it," Mr Docksey said.

"We've got to have a satisfactory discussion about this."

The motion that was adopted on Monday night included a final clause that any changes to flags at the memorial will be done in consultation with the Albury RSL sub-branch.

Albury Council chief executive Frank Zaknich told the meeting that the NSW RSL supported flying Aborignal and Torres Strait Islander flags at commemorative services, in line with national flag protocols.

Mr Docksey told The Border Mail on Tuesday that such protocols were irrelevant to the debate around flags on Monument Hill because they were a "local issue not a state issue".