Tincknell began his motorsport career in karting in 2001 , where he was active until 2008. In 2008 he switched to the single-seater racing and competed in the Winter Championships of the British and the Portuguese Formula Renault . In 2009 he competed for CRS Racing in the British Formula Renault. With two second places as the best results, he finished the season in fifth place overall. He won the subsequent winter championship of the British Formula Renault. He also took part in two races of the northern European Formula Renault . In 2010 Tincknell stayed with CRS Racing in the British Formula Renault. Although he scored two wins and was again fifth in the championship.
In 2011 Tincknell moved to Fortec Motorsport in the British Formula 3 Championship . With a win, he finished the season in eleventh place in the championship. During test drives at Spa-Francorchamps after the season , Tincknell had an accident in which he broke his finger. The connection between finger and hand was severely affected. After intensive medical treatment, Tincknell completed his second British Formula 3 season for Carlin in 2012 . He won four races and achieved nine podium finishes. While his team-mate Jack Harvey won the championship, Tincknell was fifth overall. He also made three guest starts in the Formula 3 Euro Series .
In 2013 Tincknell moved to the European Formula 3 championship together with Carlin . He won a race and was on the podium three times. As the best Carlin driver, he finished the season in fifth place in the overall standings.