Flanagan joined Dan Agger's HBK last season, but his campaign was hit by injuries, restricting him to just four appearances.
HBK chief Per Rud said: "Unfortunately, it did not turn out as we had hoped. It's no secret. We knew that Jon Flanagan had not played continuously when we picked him up, but he came fine from the start, and was so unlucky to run into a nagging injury.
"It unfortunately came to characterise the rest of his time here. We therefore chose to sit down and look each other in the eye, and we have agreed that it is best to stop working together here. It gives Flanagan peace of mind to consider his football future."
Flanagan also said: "HB Køge is a fantastic club, which I have enjoyed being a part of. I have huge respect for Daniel Agger. He is a great coach and a great man. I would like to thank my teammates who have made me feel welcome and I have established good friendships here.
"The club has great potential and looks into an exciting future. Unfortunately, injuries have made it hard for me to get rhythm into my game. I wish HB Køge all the best in the future."