Born in Glasgow, Kinniburgh began his career with Rangers,[2] and in December 2008 he joined Queen of the South on loan for two months.

[5] In August 2009, he joined Oxford United on loan along with fellow Rangers reserve player Ross Perry.

[10] He returned to his parent club after the loan ended, but on 27 January 2012, it was announced that his contract with Oxford would be cancelled by mutual agreement.

[13] On 6 June 2013, Kinniburgh moved to Kettering Town where he finished the 2013/14 season as club captain and appeared in all 42 league matches.

[14] On 17 December 2016 it was announced, that Kinniburgh had signed for Corby Town as a player-coach for the first team under manager Gary Mills.