Born in Blackpool, Lancashire, Blinkhorn started his career with hometown club Blackpool. He played as a substitute in the victorious 2004 Football League Trophy Final. On 22 November 2006 he was loaned to Bury, but Blackpool manager Simon Grayson included a 24-hour recall clause in the contract, which began 28 days into the loan period. The loan period was due to end on 22 February 2007, but Blackpool cut it short and he returned on 9 February.
He was loaned to Morecambe of the Conference National for a month on 2 March 2007. Blinkhorn made an immediate impact, scoring the first goal in a 2–0 victory over St Albans City. By the end of his loan stint he had scored eight goals in 12 games.
Blinkhorn joined Morecambe on a permanent basis on 28 June 2007, for a fee of tribunal-set fee of £15,000, plus 25% of any future transfer fee that Morecambe were to receive for him.
He was released by Morecambe in May 2009, and joined League of Ireland Premier Division side Sligo Rovers two months later. He made his debut for Sligo as a substitute in a 3–0 home defeat against Cork City at the Showgrounds on 12 July and scored his first goal for the club two weeks later in a 2–0 win over St Patrick's Athletic at home.
After the signing of Shamrock Rovers striker Pádraig Amond in the pre-season of 2010, Blinkhorn had to be second choice for half of the season until Amond signed for F.C. Paços de Ferreira. On 25 September 2010, Blinkhorn scored the winner for Sligo in a 1–0 win against Monaghan United in the 2010 League of Ireland Cup Final. He had to sit out Sligo's penalty shoot-out win over Shamrock Rovers in the 2010 FAI Cup Final on 14 November through suspension, along with recently confirmed PFAI Player of the Year, Richie Ryan.
Following the expiration of his Sligo contract, Blinkhorn returned to England after signing for Conference Premier side York City on a contract until the end of the 2011–12 season on 10 January 2012. He scored four minutes into his debut against Salisbury City in the FA Trophy second round on 14 January 2012, having entered as a 65th-minute substitute, with York's fifth goal in a 6–2 victory. His first and only league goal for York came with the winner in the sixth minute of stoppage time at home to Stockport County on 18 February 2012 after heading in Jamie Reed's bicycle kick. Having been uninvolved for York in their play-off games, which concluded with League Two promotion, Blinkhorn finished the season with two goals in 19 appearances for York. He was released on 3 July 2012.
After trials with Barrow and Chester, Blinkhorn signed for Conference Premier side Hyde on 17 August 2012. He scored on his debut for the club later that day, putting Hyde into the lead in a 2–1 defeat at home to Luton Town. He finished the season with Hyde having scored seven goals in 30 games.
In April 2013, he joined AFC Fylde on loan. Scoring two goals in three games including the opening goal against Hednesford Town in the Northern Premier League Premier Division play-off semi-final. On 25 June 2013, Blinkhorn signed a permanent one-year deal with Fylde.As of match played 4 May 2013.
BlackpoolFootball League Trophy: 2004
Sligo RoversFAI Cup: 2010, 2011
League of Ireland Cup: 2010