Born in Cambridge, Cambridgeshire, Wilkin started his career with hometown side Cambridge City, before moving into the Football League with Northampton Town. Later spells followed with Rushden and Diamonds, Nuneaton Borough, Cambridge City and Grantham Town, before returning to Nuneaton as player/assistant manager to Roger Ashby in 2004. Following the sacking of Ashby in 2006, he was appointed caretaker manager and was subsequently given the job on a permanent basis. After Nuneaton Borough were liquidated at the end of the 2007–08 season he was appointed manager of the reformed club, now known as Nuneaton Town. He guided the team to a second place finish in the Southern League Division One Midlands and promotion at the first attempt, beating Chasetown in the play-off final. The next season he guided the team to a second successive promotion, beating Chippenham Town in the play-off final after finishing second in the Southern League Premier Division. In 2012, Nuneaton Town finished the season in fifth place in the Conference North and won the play-off final, after beating Gainsborough Trinity 1–0, guiding them back to the Conference Premier after a nine-year absence.
Wilkin was appointed manager of Nuneaton's Conference Premier rivals Wrexham on a two-year contract on 20 March 2014. In his time at the Welsh club so far he has released Robert Ogleby, Kyle Parle, David Artell, Jay Colback and Joe Anyinsah, as well as Kevin Thornton (who has now joined league rivals Tamworth FC) and Stephen Wright who he has invited back for pre-season training to try and earn themselves a deal. His latest moves on restructuring for the 2014/15 campaign seen Kevin bring in young centre-back Blaine Hudson from League Two side Cambridge United FC and winger Wesley York from his old side Nuneaton Town FC. Kevin has also added to his back-room staff in the appointment of Gary Mills as Assistant Manager. Gary knows Kevin from his playing days at Liberty Way where he played under his management. In an interview in June 2014 Kevin said "I am comfortable with the way things are shaping up so far in the transfer market. I have shown a handful of possible signings around the stadium and Colliers Park over the last few days and I am happy with the state of play as I talk to you now."