Port Vale
Kirkham was born in Cobridge, Stoke-on-Trent, and progressed from a promising schoolboy footballer through Cobridge Church and Congleton Town, before heading to Sheffield to go through teacher training. Upon his return numerous clubs approached him, but Kirkham joined local side Port Vale after a successful trial in April 1920.[3]
He turned professional in August 1923, making his debut on 27 October at Elland Road in 3–0 defeat by Leeds United.[4] He scored his first senior goal on 19 January 1924, in a 3–1 win over Coventry City at Highfield Road.[4] On 8 March, he scored twice in a 3–1 win over Fulham at The Old Recreation Ground. He went on to finish the 1923–24 season with seven goals in 21 Second Division games.
He quickly became virtually the Vale's only source of goals, and hit 33 goals in 44 games in 1924–25 – more than the rest of the squad combined.[4] He scored his first hat-trick in the FA Cup, in an 8–2 demolition of non-League Alfreton on 13 December. He also hit hat-tricks in the league against tougher opposition, bagging three against both Clapton Orient and Stockport County. As well as this he hit the net twice in a 7–2 defeat to First Division club Aston Villa at Villa Park, in the First Round Proper of the FA Cup.
On 7 September 1925, Kirkham scored a hat-trick in a 3–0 victory over rivals Stoke City at the Victoria Ground. This completed the double over Stoke, as he scored twice in a 3–0 home victory eight days previously. On 19 September, he hit the net four times in a 6–1 thrashing of Darlington. He was called up to represent a Football League XI against an Irish League XI in October 1925 at Anfield, where he scored twice in a 5–1 victory.[4] He scored hat-tricks against Middlesbrough and Preston North End, and finished the 1925–26 campaign with 35 goals in 41 appearances.
In the 1926–27 season, Kirkham scored a club record 38 league goals, in a total of 41 goals in 46 league and cup games.[5] He hit hat-tricks against Grimsby Town, South Shields, Notts County, and Middlesbrough, and also hit four in a 7–1 win over Fulham. In the FA Cup, he earned the Vale a replay against Arsenal with the equaliser in a 2–2 draw, before the tie was lost at Highbury.
He never rediscovered his record-setting form, though still managed to hit 14 goals in 40 games in 1927–28. He also found himself briefly rested, as Stewart Littlewood found a short period of good form. Though he scored 15 goals in 32 appearances in 1928–29, hitting a hat-trick against Reading, the club suffered relegation into the Third Division North. Kirkham remained in the Second Division, after he transferred to Stoke City for a £2,800 fee; this was a club record for Stoke.[6]