The son of former manager Ken Brown , Kenny has been somewhat of a footballing nomad. He began his professional career at Carrow Road in 1985 and made his league debut as substitute for Wayne Biggins at home to Oxford in November 1986. Although primarily a right back, Kenny was able to play on either flank. Despite this ability, he was unable to displace Mark Bowen and Ian Culverhouse from the full back positions.

After his father's dismissal as manager, Kenny felt uneasy at Norwich and transferred to Plymouth Argyle in August 1988. He had made 28 appearances for the Canaries. He enjoyed his spell on the South Coast notching up 126 league appearances in which he scored 4 goals. He was the Pilgrims' Player of the Year in 1990/91 which prompted a move to his father's old club West Ham United in August 1991. Although officially a Hammer until January 1997, he made just 63 league appearances for them in this five year period. Rather than frequent the reserves, Kenny spent time on loan to Huddersfield (5 games), Reading (12 games, 1 goal), Southend (6 games) and Crystal Palace (6 games, 2 goals) where his goals helped Palace to the Division One play-off finals at Wembley. Another spell on loan to Reading generated another 5 league appearances before Birmingham City paid £75,000 for his services in January 1997. 11 games for the Midlands side was followed by a £60,000 (£40,000 + £20,000 after 20 games) move back to London with Second Division Millwall in the summer of 1997.

In a recent survey by Hammers magazine, Kenny was surprisingly rated by West ham supporters as their 49th all-time favourite player. He was also named as scorer of the 14th best ever goal scored by West Ham for his effort against Aston Villa in August 1991 [Hammer News August 2000]

Kenny was given a free transfer by Millwall in March 1999 who hoped he would find a new club before transfer deadline day. Kenny was fortunate to do so and joined Gillingham. The Gills released him at the end of the 1998/99 season with Kenny making just 4 appearances. Kenny embarked on a trial with Colchester in September 1999 following an injury to Steve Forbes. The March 2000 edition of Hammers magazine reported that Kenny had returned to Upton Park to train with West Ham before dropping into non-league football with Kingstonian of the Football Conference.

On 23 July 2000, the Non League Paper reported that Kenny had joined Welsh side Barry Town as player-coach under new manager Peter Nicholas (of Arsenal, Chelsea, Crystal Palace and Wales fame). Prior to this move, Kenny had played in Ireland with Portadown. Kenny became caretaker manager at Barry towards the end of September 2001 when Peter Nicholas departed to become Colin Addison's Number Two at Swansea. Ken's position was made permanent in October 2001 and Barry went on to win the Welsh League earning Brown a crack at European glory. They also won the Welsh Cup. The following season saw Barry win the double again - the cup win coming in a 4-3 penalty shoot-out against Cwmbran. As a result he was named the Loosemores Solicitor's Manager of the Season for the JT Hughes Mitsubushi Welsh Premier League - an honour he had shared the previous season. Kenny then announced that he intends to cut back on his playing during the next season (2003/04) to concentrate on management especially in European competition.

The opening weeks of the 2003/04 were full of turmoil for Barry. Chairman John Fashanu quit and the club faced debts of £1million stretching back over many years. Unable to pay their players, the game against Connahs Quay Nomads was cancelled on 23 August 2003 as Barry could not raise a side. The following week saw Kenny and his remaining seven professional players (some had been sold) turn up to the club only to find themselves locked out by the new consortium that had bought the club. Kenny resigned as manager only for all the players to be told that they were all to be released. Barry then went to register 22 new players in order to fulfill their fixture against Caernarfon on 30th August but they lost 8-0. The new consortium named former Aston Villa and Shrewsbury defender David Hughes as the club's new manager. Kenny Brown told the Non-League Paper that his players and he had contacted the Football Association of Wales and the Professional Footballers' Association over this situation and their lack of wages over the previous two and a half months.

Kenny returned to his East London roots signing for Ryman Leaguers Tilbury at the beginning of December 2003 alongside former Ipswich star Mark Brennan. He then moved to Spain playing for FC Torrevieja, located an hour south of Benidorm and playing in the Spanish equivalent of the Conference North. Kenny was the only Englishman in an entirely Spanish line-up. The club have an average attendance of 3000 - mainly drawn from the 20000 British ex-pats living in the region. Dag T Hoelseth of the Norwich City Supporters' Club of Scandinavia informed me in August 2005 that Kenny has decided to retire from playing but now coaches their reserve team playing in the Valencian Regional League.

In May 2006, Kenny was appointed Director of Football at FC Javea who play in the Valencian Preferent League. He will also run a summer school in Javea during the summer of 2006 with former Hammer Julian Dicks

When Dicks was appointed manager of Conference side Grays Athletic in September 2009, Brown was appointed as his assistant.

He was appointed as assistant manager of Concord Rangers in June 2012. The following month, he joined Barnet as Lead Development Coach. At the end of the 2012/13 season, Barnet were relegated to the Conference. Following their relegation, Brown's contract was not renewed and he departed Barnet at the beginning of May 2013.

On 30th July 2013, Brown was appointed as Assistant Manager to Dean Holdsworth at Conference side Chelmsford City. During the autumn of 2013, Brown stepped up to become caretaker manager for four games but left after Chelmsford appointed Mark Hawkes as the club’s new first-team manager and Steve Smith as assistant manager on 28th November 2013.

He then joined Dagenham & Redbridge as Academy Manager on 16th July 2014.

When Dagenham were relegated to the Conference, they disbanded their academy. Brown then joined Millwall in the summer of 2016 as their Head of Coaching

Brown left Millwall at the end of December 2021 to join his old club West Ham as Head of Coaching for the Under-9s to 14s. West Ham have split the traditional Head of Coaching role in two. While Brown will have responsibility for the 9s to 14s, Kalam Mooniaruck will oversee the 15s to 18s

On 7th November 2022 he was appointed as Interim Academy Manager replacing Ricky Martin who had left to join Stoke. He will be supported in the forthcoming period by Head of Coaching Development Kalam Mooniaruck. Brown said: “I am very honoured and proud to have been asked to step into this role for the interim period at West Ham United's world-renowned Academy, which I believe will help us to ensure continuity and, most importantly, consistency and familiarity in the development of our young players.