Francis Dominic Kelly was born on 11 October 1923 in South Shields, County Durham. He was the eldest of two sons born to James Terrence Kelly and his wife Catherine.

Before enlisting, Francis worked as a shop assistant. He enlisted into the Army on 5 February 1942 and joined The Royal Armoured Corps. He was initially posted to 58th Training Regiment and joined 1st Northamptonshire Yeomanry on 4 September 1942 after the completion of his training. On 5 February 1943 he qualified as a Gunner Mechanic. 

Francis embarked for Normandy on 13 June 1944. In July 1944 the battalion took part in Operations Charnwood and Pomegranate.

On 13 August 1944, 1st Northamptonshire Yeomanry joined up with 5th Battalion The Seaforth Highlanders for Operation Kummel. The north flank of 2nd Canadian Corps drove towards Falaise and was to be approached by the Americans in the south.

On 14 August 1st Northamptonshire Yeomanry moved forwards through Saint-Sylvain, to the north of Le-Bu-sur-Rouvres. By 21:00 hours 5th and 2nd Battalions of The Seaforth Highlanders had reached their objective and had moved through Glatigny, north of Condé-sur-Ifs.

On 15 August 1st Northamptonshire Yeomanry pushed over the river to Escures-sur-Favieres. It was during their advance on 15 August 1944 that Trooper Francis Kelly went missing. He was 20 years old.

As Francis had been listed as missing, his name was commemorated on the Bayeux Memorial in Normandy. His final resting place was identified when a researcher submitted information that was confirmed following additional investigation by the JCCC, CWGC and the National Army Museum.

Francis' final resting place was rededicated in a military ceremony on 26 June 2025 at CWGC Banneville-la Campagne War Cemetery, France and marked with a newly inscribed Commission headstone to be cared for in perpetuity.