McKenzie joined Noriwch City on trial from Tottenham in March 2010,
playing in the 2-1 defeat at home to Watford on 20th March 2010.
He was then offered a place in City's academy from July 2010 which
Taylor was named the academy's player of the season for 2011/12
Taylor signed for Sheffield Wednesday on 22nd October 2012 on a
one year contract, following a successful trial with the Owls' development
On 14th September 2013, McKenzie joined Conference North side Gainsborough
Trinity on loan.
Despite not playing a single first team game for Wednesday, Notts
County signed him on a two year deal on 21st May 2014.
On 24th March 2016, he joined non-league Corby Town on loan until 30th April 2016.
McKenzie was released by Notts County on 20th May 2016 along with ten colleagues. He joined Chesham United on 3rd October 2016. He then joined Enfield Town for the 2017-18 campaign, when he made thirty five appearances and helped out with four goals at the other end.
By the 2018/19 season he was playing for Isthmian League side Cheshunt. He played an enormous part in their South Central Division promotion during 2018-19, making forty three appearances, and then went on to help them establish themselves in the Premier Division, playing thirty two times before 19-20 came to a premature end and another eleven times in the tiny 20-21 campaign. In 2021-22 he helped his side to yet another promotion, playing forty one times- and notably scoring the last minute winner as the Ambers defeated Bishop's Stortford in the Play Off Semi-Final. He was then almost an ever-present in National League South in 2022/23 and played another sixteen times in 2023/24 with Cheshunt back in the Isthmian League.
At the end of December 2023 he returned to Enfield Town