A 33-year-old man has been arrested on suspicion of burglary and arson with intent to endanger life.
The investigation is part of a probe into the attack on the Alliance Party offices in Carrickfergus last Wednesday.
Elsewhere, the PSNI confirmed it is investigating criminal damage at the home of Democratic Unionist Party (DUP) councillor Sammy Brush's house overnight in Ballygawley.
The PSNI said a number of protests during the day over the flag controversy passed without incident today.
More than 20 demonstrated at the bottom of the Shankill Road in Belfast while up to 300 people gathered on the Peace Bridge in Derry.
It is understood more than a dozen of these also walked through Derry city carrying the union flag.
Yesterday, eight people were arrested yesterday on public order offences after police clashed with loyalist protesters.
Three people who were arrested on Friday, including a 13-year-old boy, have been charged in connection with the violence.
Assistant Chief Constable Will Kerr said loyalist paramilitaries had been orchestrating some of the violence seen in recent days.
The violence - which has left 27 police officers injured - overshadowed a visit to Northern Ireland by US Secretary of State Hillary Clinton.
Much of the anger has been directed towards the non-sectarian Alliance Party, whose councillors in Belfast voted to limit the number of days the union flag could be flown over the city hall from 365 to 17.
A death threat was made against the party's only British MP, Naomi Long, while a constituency office in Carrickfergus, Co Antrim, was destroyed in an arson attack and three councillors had their homes vandalised.
Belfast City Councillor Laura McNamee was also advised to leave her home.
How to stop the street violence which has followed the union flag decision is a challenge.
The advice of the main unionist leaders is being ignored and the police are not sure who, at community level, can influence the rioters.
A man who briefly addressed the demonstration outside Belfast City Hall yesterday afternoon, and described himself as "an ordinary Protestant, a normal guy from Comber (Co Down)", is attached to an organisation called ‘Britain First’.
In the past Jim Dowson has spoken at events linked to the British National Party.
Mr Dowson suggested that he had just come along to yesterday's demonstration with his “son and his daughter-in-law but just got roped into it.”
When asked how he got involved in the rally, he said he had been sitting in the house on Monday night when he saw the flag being voted to come down.
After addressing the rally he gave out leaflets which included the phrase “Smash the Alliance Party”.
When interviewed by RTÉ's Northern Editor Tommie Gorman, Mr Dowson said: "You are from an Irish station. How would you like it if we said 'right, if we are going to have mutual respect, we want to take the tricolour down from Dáil Éireann’.
“You'd go off your head, and we are going off our heads because it is not right.
“If are going to be part of a shared future and share this island in peace together, we need to have mutual respect.
“And that means you have your flag up in Dublin and we have our flag up in Belfast. Then we can live in peace."