Marc Karun was arrested in Maine as he left his home, police in Norwalk, Connecticut, told CNN. Karun is being held at the Penobscot County Jail in Bangor, Maine, and will make an appearance in court on Friday afternoon.
It is unclear whether he has legal representation at this time.
Karun was convicted of sexual assault in Connecticut in 1989 and is listed as a lifetime registrant on the Maine sex offender registry.
On September 23, 1986, Flynn said goodbye to her friends and started off on the path she normally took to get home from school, according to WTIC. When she didn't return home on time, her mother started to worry and eventually reported her missing.
Flynn's body was found in a secluded area about 12 hours later, about 100 feet off the path she took home from school, the station reported.
Flynn's family commented on the arrest in a statement.
"We wish to thank the Norwalk Police Department for bringing Kathleen's murderer to justice," they said. "This continues to be a very difficult time for us and we do not wish to make any further comments. We ask the media to please respect our privacy."