The assembly's Department for Finance and Personnel (DFP) has approved the move for five buildings under its control.
The flag already flies at four DFP buildings; Academy House, Ballymena; Colby House, Belfast; Queen's Court, Queen's Street and at the department's headquarters at Craigantlet Buildings on the Stormont Estate.
Work is underway so the flag can fly at an additional five buildings: the DoE offices on College Street, Goodwood House and Victoria Hall, both on May Street, Clare House on Airport Road West and Rosepark House in east Belfast.
A department spokesperson said that a regulation "gives the discretion to fly the union flag" at government buildings on specified days.
"The Finance Minister has confirmed he wants the Department to fly the union flag at buildings where we have Premises responsibility," they explained.
They said that the estimated cost per site ranged from £500-£2,000 depending on "the complexity of works required at each site - location of flagpole, structural issues, site preparation works required etc".
The spokesperson confirmed work to erect the flagpoles should be completed within four months.
After months when people have been losing hope and have been losing confidence in government, and after last week’s trauma on care homes, the Finance Minister and DUP confirm what is their priority.
Environment Minister Alex Attwood
Sinn Féin North Antrim MLA Daithí McKay has stated that Sinn Féin will be seeking legal advice over the Finance Minister's order, which he said was "deliberately provocative".
"There are extremely pressing issues to be dealt with by the Assembly such as the fiasco around the closure of care homes, the Welfare Reform Bill or creating jobs and employment. All of these are worthy of spending public money on," he said.
"In recent weeks officials from the Department of Finance were in front the Finance and Personnel committee at Stormont explaining that they could not even carry out proper assessment of public sector pension reforms due to the fact that it would cost £10,000 yet the Finance minister can spend that exact amount of money on a divisive pet project.
"Instead of giving issues like this priority the DUP Minister has placed a party political project first."
Environment minister Alex Attwood said the move "raises again fundamental questions about Sammy Wilson's and the DUP's judgement".
His department's office at College Street is one lined up for a new flagpole.
He said: "The DUP is making a bad situation worse. We should be working through the flags issue wisely and together."