Robert Fleck began his footballing career with Scottish giants Rangers but despite winning Scottish under 21 caps whilst at Ibrox, he was never guaranteed a first team place. In 4 years, he made 85 appearances, scoring 29 goals. On 16th December 1987, Norwich manager Dave Stringer paid £580,000 to bring Fleck to Carrow Road although reports from the time suggest that Stringer was initially interested in fellow Rangers striker Mark Falco. He made his debut against Wimbledon two days later.

Whilst in his first spell with Norwich, Fleck quickly became a fan favourite. He was leading scorer for four consecutive seasons scoring a total of 66 goals in 181 appearances (15 as substitute). Mike Davage's Glorious Canaries states that "you name it and it happened to him during his stay at Carrow Road as he had a court case, various club fines, injuries (four knee operations and broken ribs), transfer requests and constant speculation on whether he was staying or not and goals galore". He was also sent off three times but won Scottish full international honours including playing in the 1990 World Cup finals in Italy.

In August 1992, he joined Chelsea for £2.1 million but this big money move was not successful. He never fitted in at Stamford Bridge and found goals hard to come by. He made just 40 appearances for the London side scoring a paltry 3 goals. He spent time on loan to Bolton (7 appearances, 1 goal) and Bristol City (10 appearances, 1 goal) before returning to Carrow Road on loan in August 1995. This transfer was made permanent on 28th September 1995 for a fee of £750,000. He never enjoyed the same success in front of goal as in his previous stint at Carrow Road and added only 18 goals since his return. He played a deeper role in his second spell at Norwich acting as a provider and as inspiration for the younger players. In January 1998, Mike Walker announced that Fleck would not gain a new contract in the summer but this did not deter Fleck who continued to give his all for the Norwich cause. In a disappointing season where many players did not look as if they cared for the club, Robert's enthusiasm was respected by the Carrow Road faithful.

In the Pink Un of Saturday March 21st 1998, Flecky recalled his some of his Canary memories. They were

• his first goal at Carrow Road on March 5th 1989 and was the only goal of the game against Manchester United.
• the injury time winner in the televised clash with Millwall on January 22nd 1989
• the goals scored against Manchester United on January 21st 1990 soon after the birth of his daughter Olivia.
• The brace netted against Liverpool in a 3-0 victory on February 22nd 1992
• the 1989 FA Cup semi-final against Everton which he missed due to his father's death the previous night
• being ruled unfit to play in the 1992 FA Cup semifinal against Sunderland due to his damaged ribs.

Thursday 26th March 1998 saw the end of striker Robert Fleck's second spell at Carrow Road. The Glaswegian striker signed for Division One strugglers Reading for £50,000 on transfer deadline day having fallen out with Canary manager Mike Walker. This Canary legend departed the club with 299 first team appearances to his name. However his spell in Berkshire was not productive and on February 18th 1999, it was announced that he was retiring from football due to a back injury.

Upon retirement, Robert teamed up once again with Dale Gordon at Gorleston with Robert helping with the coaching. He made his debut for the Greens against Ely on 13th March 1999 in a 3-0 victory. Making an impression on the East Coast, Fleck was named by Teamtalk as a potential successor as Norwich City manager following Bruce Rioch's resignation on 13th March 2000.

Following Gordon's departure from Gorleston to head up part of Ipswich's youth academy, Robert became player-manager of the Greens. He won his first trophy as a manager in his first season in charge when in April 2001 he led Gorleston to a 4-0 victory in the Norfolk Senior Cup final against arch rivals Great Yarmouth Town who fielded former Canaries Greg Downs and Robert George. This victory was no flash in the pan as Flecky's Gorleston side finished runners-up to Sudbury in the Jewson League.

In March 2002, Robert was linked by the Eastern Daily Press with a switch to manage Jewson league rivals Diss Town following the resignation of Alan Biley but this was dismissed as speculation. However he announced in April 2002 that he would resign as Gorleston's manager at the end of the 2001/02 season. By the end of April, he had confirmed that he would take over as Diss manager at the end of the season, proving that there is a grain of truth in media speculation sometimes.. He had been approached by bigger clubs in higher divisions but did not wish to uproot himself or spent considerable time travelling. Flecky combines his management career with running football schools at Hethersett and Stoke Holy Cross

Fleck won the Norfolk Senior Cup for a second time in April 2003 when his Diss side beat Great Yarmouth 4-1 with two goals from Lee Gilman and two for man of the match Coren Hardy. His Diss side started well the following season and topped the table in early weeks. However Robert has sought new playing experiences. In September 2003, he signed for the Suffolk Punch Pub in Westwood Avenue, Lowestoft, which has Ipswich Town FC's symbol emblazoned on their sign! The team play on Sundays in the Division Three Lowestoft Sunday League

Fleck's Diss Town side won the Norfolk Senior Cup again in May 2005 beating Wroxham 3-0 in the final at Carrow Road with goals from David Tyrie(OG), Coren Hardy and Matthew Wright. A poor season in 2005/6 saw Robert contemplating his future at Diss in the summer of 2006. A run of poor form saw Fleck sacked by Diss on 18th October 2006.

Fleck returned to employment with Norwich City in May 2007 when he joined the club's scouting network.

The Evening News revealed on 21st November 2008 that Fleck is currently working as a teaching assistant at Parkside School in Norwich

He is also now covering the non-league game for Norwich as part of Ewen Chester's scouting team.