Born in Liverpool, Jennings played youth football at Liverpool before being released as schoolboy. He soon joined Tranmere Rovers aged 15, having played for other clubs and having visited Rovers for a trial.
He made his club and Football League debut on 18 September 2010 in Tranmere's 1–1 draw against Charlton Athletic, coming on as a second-half substitute. On 28 September 2010, he scored his first goal for the club in a 1–0 win against Bristol Rovers in his third senior match for the club. Jennings followed this up a few games later with a brace and two assists in the 4–2 victory over Milton Keynes Dons. On 13 November, Jennings scored a winner against Plymouth Argyle with a twisting run from the halfway line.
In October 2010, Jennings received the award for Apprentice of the month from the PFA.
His goal against Plymouth helped attract interest from larger clubs, and Tranmere rejected an offer for Jennings from an unnamed Premier League club in the 2011 January transfer window. In March 2011, he was voted League One Apprentice of the Year at the Football League awards.
In July 2011 Jennings was signed by German club Bayern Munich where he would initially play for Bayern Munich II the reserve team in the Regionalliga Süd. In late October 2011, Jennings' habituation into Germany was hindered after he suffered multiple ligament tears in his knee, sidelining him until March 2012. On 11 October 2012, Jennings scored his first goal in a Bayern shirt in a 2–0 friendly win over SpVgg Unterhaching. On 27 October 2012, Jennings scored his first competitive goal in Germany in a 2–1 loss away at Würzburger Kickers, with his second following just six days later in a 2–2 draw at FC Augsburg II.
On 18 June 2013, it was confirmed Jennings had signed for Barnsley on a three-year deal for a fee of £250,000 from Bayern Munich. Upon arriving, Jennings spoke of disappointment of having not broken into the first team squad at Bayern Munich and his excitement at Barnsley and his eagerness to do well there.
On 3 August 2013, he made his Barnsley debut against Wigan Athletic, coming on as a substitute in the second half for Tom Kennedy; however, he was sent off just five minutes after he came on, having misjudged a challenge on Wigan's James McArthur. Subsequently, he was suspended for the following three games. While suspended, Jennings scored a hat-trick for the reserves, and he scored his first senior goal for the club on 8 March 2014 in a 1–0 win against Nottingham Forest.
On 28 November 2013, Jennings joined Milton Keynes Dons on loan until 5 January 2014. On 30 June 2015, following his release by Barnsley, Jennings signed for Championship side Milton Keynes Dons on a one-year contract.
On 1 February 2016, it was announced that Jennings had left the club by mutual consent.