His great nephew, Joe Kendrick Jr., also showed potential as a footballer and as youth was contracted to both Newcastle United and TSV 1860 Munich.
As a member of the squad that competed at the 1924 Olympic Games, he made his debut for the Free State against Bulgaria in their first ever senior international on 28 May.
Together with Mick O'Brien, Harry Duggan and Tommy Muldoon, he became one of the first four English League based players to play for the Irish Free State.
On 25 February 1934 at Dalymount Park, together with Paddy Moore and Jimmy Kelly, he was a member of the Free State team that made its World Cup debut in a qualifier against Belgium.
With the Free State trailing 4–3, in the 75th minute, a corner from Kelly was cleared only as far as Kendrick who then lobbed it towards Moore who then scored a dramatic equaliser.