The authority will hold public meetings between 16 November and 7 December to discuss services which could be cut.
It believes it has found two-thirds of the £21m savings needed in the next financial year, but it still needs to find a way of slashing £7m more.
Councillors and officers hope residents can help persuade the Welsh government to reduce the impact of the cuts.
Council leader Aaron Shotton said: "We are trying to put up an argument and stand up for local services and not simply passport through austerity cuts.
"There's a window of opportunity to save services in Flintshire."
The council has previously warned it cannot find ways of saving the money and that, if the government cannot be persuaded to limit the loss to Flintshire's grant, then services may be at risk.
It has suggested the grant to Clwyd Theatr in Mold could be withdrawn, bins may be emptied less frequently, leisure centres could be closed and winter road gritting could be cut to a minimum.
Flintshire residents have been invited to help save services threatened by £21m of council spending cuts.