Lieutenant Greer was the only son of a prominent Ballymoney solicitor. On 13 or 14 August 1914 he enlisted as a Private in the North Irish Horse (Service No.1006) and embarked from France with C Squadron a week later.

He was commissioned to the 3rd (Prince of Wales) Dragoon Guards on 6 December 1914, and was later attached to the 1st Battalion, Irish Guards.

The information in the three paragraphs below is sourced from Robert Thompson's Ballymoney Heroes:

In early March [1915] a bullet struck the scoop of his cap, passed through his hair, and came out through the back of his cap without injuring him. ... On 18th May 1915, at the Battle of Festubert, Lieut Greer sustained a number of bullet wounds, the worst being damage to his right hand, for which he was transferred to a London hospital. ...

In January 1916 he was awarded the Military Cross. Greer was seriously wounded on 15 September 1915 during the Battle of the Somme. According to Private Joseph Doherty:

On the morning of the 15th September last we were at Ginchy and our objective was a small village called Flers. The Coldstreams led the attack and we followed and the supports were the Scots Guards and the Grenadiers. When we got to the first line of the enemy trenches we stopped a few minutes. Lieut Greer then led us to the second line of trenches. He had a revolver in one hand and a stick in the other, and rushed in front pointing his stick towards the enemy, and shouting to us to come on. It was between the trenches he got hit in the head, and fell. He gave his revolver to Sergeant Hugh Carton and told him to 'carry on'. Carton then told us to follow him, and that we did, right into the German third line.

Greer was evacuated from the battlefield but on 3 October 1916 he died in N.2 Red Cross Hospital, Rouen. He was aged 31.

Lieutenant Greer is buried in St. Sever Cemetery, Rouen, Seine-Maritime, France, grave A.11.2.

The gravestone inscription reads:

LIEUTENANT

J. KENNETH M. GREER MC.

IRISH GUARDS

3RD OCTOBER 1916 AGE 31

HE COUNTED NOT HIS LIFE

DEAR UNTO HIMSELF