The Loyalist Community Council (LCC) has created the flag to commemorate the centenary of the World War One battle.
It says the flag is supported by three paramilitary groups, the Ulster Defence Association (UDA), the Ulster Volunteer Force (UVF) and the Red Hand Commando.
"We hope this is the only flag that is flown along arterial routes alongside the Union flag and the Ulster flag," Winston Irvine of the LCC said.
"I think this flag will hopefully reduce the amount of perceived paramilitary flags."
Mr Irvine said he did not expect nationalists "to be screaming in support of the flag from the rooftops".
But he added: "I do hope people see this is an attempt to lessen the impact of flags and to command a wider support for the respectful and dignified commemoration to mark the anniversary of the Somme.
"The Somme means something to everyone, regardless of your community background, both in Northern Ireland and in the Republic of Ireland, given the scale and severity of that battle on the people of this island."
Members of the 36th Ulster Division were among 100,000 Allied soldiers who fought at the Somme in 1916.
A private benefactor has paid for the purchase of the flags.
The group has also drawn up a set of protocols for the flying of flags.
Mr Irvine said people were "fed up with torn and tattered flags flying from lamp posts and buildings".
The protocols give guidance on the period of time flags should be flown, suggesting a three-month spell starting in June.
Assistant Chief Constable Stephen Martin of the Police Service of Northern Ireland said the flying of flags in public places "provokes a range of strong responses and very different viewpoints".
He added: "We hope [the LCC's new flag and its protocols] can be a positive development in improving the overall context in which flags are flown."
A new flag to mark the Battle of the Somme has been unfurled in Belfast.