Councillor John Hussey said the decision to only fly the flag on designated days is in breach of BCC's equality scheme.
He said the complaint is the first step towards possible legal action.
"We believe that both in its processes and in its decision over the removal of the Union flag Belfast City Council made multiple breaches of its published and legally required equality scheme," said Mr Hussey, who is secretary of the DUP group on the council.
"The DUP is committed to pursuing all political avenues to overturning the disastrous decision by Sinn Féin, SDLP and the Alliance party and to repairing the harm to good relations and a shared future it has caused.
"As with the launch of the Unionist Forum, through this initiative my party wishes to demonstrate that there are political alternatives to protests and most especially to violence."
This is the first step towards a formal complaint to the Equality Commission and ultimately possible legal action
The change to the flag policy was endorsed by nationalists and the cross-community Alliance Party at the start of December, and opposed by unionists.
Since then a number of loyalist protests have been held across Northern Ireland and many have been followed by violence, including six nights of rioting in east Belfast this month.
Over 65 police officers have been injured during the trouble.
The Alliance Party, which controls the balance of power on Belfast Council, has said the designated days option was in line with the recommendation from the Equality Commission as an approach which would promote good relations between both sides.
Meanwhile, a Belfast City Council spokeswoman said: "The decision to introduce the policy of flying the Union flag at City Hall was taken democratically by elected members at the monthly meeting of Belfast City Council on 3 December.
"The council has taken legal advice throughout this process and the decision is in keeping with the outcome of the equality impact assessment that was undertaken in line with the advice of the Equality Commission.
"The designated days agreed are in keeping with those notified by the UK Government's Department of Culture, Media and Sport."
Councillors in Craigavon have voted to review their flag policy, which could lead to the Union flag being displayed all year round rather than the current designated days.
Meanwhile on Limavady council, nationalists defeated a unionist motion to start flying the flag there on designated days.
Another series of loyalist flag protests - dubbed Operation Standstill - took place across NI on Friday night.