Kinsella joined Colchester United as a 17-year-old (he was actually signed by the legendary ex-Rangers manager Jock Wallace) and played there for seven seasons, including two in the Vauxhall Conference, and played at Wembley in 1992 when Colchester won the FA Trophy. He was nicknamed "Sheedy" by the fans, in honour of the Everton player, and is among the club's most revered former players.
He moved to Charlton Athletic in September 1996 for £150,000. At Charlton he captained the team to a dramatic victory over Sunderland in the 1998 Division 1 Play-off Final, with Kinsella scoring one of the penalties in the shootout. Following relegation after only one season in the Premiership, Kinsella lifted the First Division championship trophy with Charlton the following year.
Kinsella is remembered by Charlton fans as a turning point in their recent history, he was the first player in the modern era to stay with Charlton when his performances placed him as a top ten midfielder in the country via the Carling Opta Stats. His skill, talent and sometimes individual carrying of the team in the 1998–99 season places him above that of Richard Rufus, Clive Mendonca, Andy Hunt and John Robinson in Charlton's list of greats in the late 90's teams. In 2001 he suffered an injury, which allowed Scott Parker to take his place in the team. Kinsella could not reclaim his place in the Charlton first team after coming back from injury, so he was sold to Aston Villa in 2002, for a fee of £1m.
Kinsella made his debut for Aston Villa on 24 August 2002 against Tottenham Hotspur. He later went on to make 24 appearances in his first season. After a good start in the first half of the 2002–03 season he rarely made an appearance in the second half of the season and had a couple injuries that set him back. In Kinsella's second season he only made two appearances and left Aston Villa mid-season in early 2004.
Kinsella moved to West Bromwich Albion in January 2004, on a short-term contract until the end of the season. He made 18 appearances for the club, helping them to win promotion to the Premiership. His only goal for Albion came in a 3–0 win over Coventry City on 6 March 2004.
Kinsella then transferred to Walsall in July 2004, signing a two-year deal. After two injury damaged seasons, Kinsella took charge of Walsall on a caretaker basis, following Kevan Broadhurst's sacking in April 2006, earning one win and suffering one defeat in his two games in charge. He continued to combine playing and coaching at Walsall before being lured back to Charlton in December 2006. His last professional match was in Walsall's League Two home defeat to promotion rivals Swindon Town on 9 December 2006. Kinsella scored two goals for Walsall, once against Merthyr Tydfil in the FA Cup, and once against Wycombe Wanderers in the league.
Kinsella won 48 caps for the Irish national team, scoring 3 times and was named Irish Footballer of the Year on one occasion. He also captained the side in a friendly against Finland in November 2000. Although rarely remembered, he formed an excellent midfield partnership with Roy Keane in the qualifying stages for the 2002 World Cup. Keane was quoted as stating that the Republic of Ireland's form during that campaign was down to the presence and performances of Kinsella. After Keane's much publicised dismissal from the squad before the 2002 World Cup, Kinsella formed a solid partnership with future Charlton player Matt Holland.
While still a player at Walsall, Kinsella took on the additional roles of reserve-team manager and first-team coach. He was appointed development coach at Charlton Athletic in December 2006, with responsibility for the development of young professional players, liaison with the academy and the managing the reserve team. After the appointment of Alan Pardew, Kinsella's role was changed to that of reserve-team manager. It was announced on 10 June 2008 that he has been given a new one-year contract at the club.
In 2008 when Alan Pardew left Charlton by mutual consent, Kinsella left his post as Reserve team manager, being replaced by U18 Youth Coach Damian Matthew, to adopt a more senior role in the first team, helping Caretaker manager Phil Parkinson, while a replacement for Pardew was found. In December 2008 Parkinson was confirmed as the new Charlton manager, and Kinsella assumed the role of first team coach permantently. He was sacked along with Phil Parkinson on 4 January 2011. He was linked with return to his former club Colchester United as manager in August 2009, but the job went to Adrian Boothroyd.