After months of speculation, Norwich completed the signing of 18 year old Peterborough midfielder Flynn Clarke on 24th June 2021.

Clarke was on the books at Peterborough from the age of nine and signed a professional contract on his 17th birthday in December 2019  He made his first team debut in a 1-0 loss to Cheltenham Town in the first round of the EFL Cup in September 2020. In his second appearance for Peterborough, an EFL Trophy tie against Burton Albion, he scored his first goal for the club. His league debut came in Peterborough's opening game against Accrington Stanley in September 2020. He had made 21 appearances for the Posh by the time of his transfer to Norwich, scoring three goals.

He is the grandson of former Northern Ireland, Peterborough and Southampton striker Colin Clarke. He was selected for the Scotland Under-19 squad in October 2020.

“I feel absolutely delighted to arrive here, I’m over the moon," Clarke told City's official website. “The club is a great club. They look at a lot of the youngsters and try to make a pathway for them." It is expected that he will initially play for Norwich's development squad.

He scored nine goals and registered three assists for the Canaries' development squad during the 2021-22 campaign.

On 11th July 2022 he joined Walsall on a season-long loan. Saddlers Hhead coach Michael Flynn was pleased to welcome Clarke to the Midlands club, where current Norwich head coach Dean Smith started his managerial career. "I'm excited to welcome Flynn to the squad. He is a very talented player and he gives us that creativity in the final third. He has a very good range of passing and he's very highly thought of at Norwich. I would like to thank Dean Smith and Norwich for helping us in bringing Flynn into the club. I'm excited to work with him."

He made three appearances for Walsall before the loan was terminated early on 1st September 2022 and he returned to Norwich.

On 25th September 2022 he made his debut for Scotland Under-21s socring in a 1-1 draw with Northern Ireland.

On 2nd September 2023 it was announced that he had joined National League side Dagenham & Redbridge on a season-long loan which was cut short.

On 13th February 2024 he was loaned to National League North side Scunthorpe.

Flynn was released by Norwich on 20th May 2024. He had spent some time in prison for driving offences. He was jailed for causing serious injury to three people by dangerous driving and was condemned by police for driving "incredibly stupidly". Cambridgeshire Police said he was driving to a rave and nitrous oxide cannisters were found in the car. He was driving a BMW 218i along the A47 at Thorney at about 14:30 BST on 30 April 2022 when he crashed into a Fiat Ducato motorhome, police said. A witness told police Clarke had been driving "erratically" before the crash, weaving in and out of lanes, with the BMW's occupants looking distracted. Clarke, a 19-year-old male passenger and a 19-year-old female passenger suffered minor injuries, but two other 19-year-old men, passengers in the back seat, received serious injuries. The motorhome driver, a 59-year-old man, also received serious injuries while his 60-year-old woman passenger suffered minor injuries.

In August 2024 Lowesfoft announced that Clarke had signed for them.