Officers raided the 22-year-old's house in Donaghadee on Wednesday morning as part of the investigation into incidents linked to the loyalist demonstrations, but he wasn't in.
At the same time, an operation was carried out at the home of Willie Frazer - one of the key organisers of the flag protests. He was arrested and remains in custody.
As officers continue to look for Mr Bryson, he came out of hiding to tell UTV that he does not plan to give himself over - and accused the PSNI of "political policing".
"I have not committed any crimes. All I have done is exercise my right to peaceful and democratic protest - I've not been involved in any rioting or any violence," he said.
"Gerry Kelly met Matt Baggott last night and he asked him to arrest people. He said that on his Twitter. Then this morning, the police tried to arrest me and Willie."
Officers from the Operation Dulcet inquiry team had the power to arrest Mr Bryson on the spot when they called at his door in North Down on Wednesday morning.
When he wasn't found there, they began looking for him - with the focus shifting a few miles away to the Kilcooley Estate in Bangor.
Police searched three offices Mr Bryson has links to, then towed away his car.
The law of the country at this time is absolutely ridiculous. This is political policing and there is no way I'll be helping the PSNI in this fascist state.
Mark Gordon, who works in Kilcooley, said: "The police came and politely asked us if they could have a check in the offices and we were more than happy to oblige, so we went through the three offices we have authority over to let them see no one was hiding on the premises.
"Jamie Bryson's car was parked here at Kilcooley Square and the police left officers in unmarked cars there with it, then they came and towed it."
A series of loyalist demonstrations have been held across Northern Ireland since December when Belfast City Council changed its policy on flying the Union flag.
Many have been peaceful, however, some have resulted in street violence - with some 150 people now arrested and charged.
For the past 11 weekends, a march has taken place through Belfast city centre and authorities have come under increasing pressure to intervene.
Parades Commission chairman Peter Osborne told UTV on Tuesday that the Saturday marches have not been notified to them and are therefore unlawful and for police to deal with.
But Mr Bryson said that he does not recognise the commission's authority.
"I don't recognise the Parades Commission, so I wouldn't be notifying them of anything anyway. I view it as civil disobedience," he said.
"Martin Luther King was technically breaking the law, but he had to stand up for what he believed in, for his rights and for his country, and people don't view him as a criminal."
Meanwhile, PSNI Chief Constable Matt Baggott has said that the laws surrounding parades that are not notified may need to be reviewed - to provide more of a deterrent against illegal protests.
"I remain concerned that the current Public Processions Act does not provide sufficient deterrence to those breaking the law," he said.
"The required standard of proof to convict is high and the Act would benefit from review."