Is it absolutely certain he died??
I've identified a CSM Robert Wilkinson in 8th Yorks, but he survived...
There's a medal card for a Robert Wilkinson, who started the war as Private 13765 in the Yorkshire regiment, and finished as 2nd Lieutenant in the Royal Air Force.
The card shows he landed in France on 26/8/15, which is the correct date for 8th Yorks. It also shows the address for medals to be sent to as 70 Milbank St, South Bank, Yorks.
Then there's an MID (Mention in Dispatches) card for 13765 R Wilkinson, which shows his rank to be Company Serjeant Major in 1917.
The relevant London Gazette entry is here
http://www.london-gazette.co.uk/issues/30434/supplements/13233The next thing I can find is
http://www.london-gazette.co.uk/issues/31072/supplements/14882"York.R. Temp. 2nd Lt. R. Wilkinson resigns his commission on appointment to RAF, 31 Nov 1918."
And then...
http://www.london-gazette.co.uk/issues/31669/pages/14925"Royal Air Force.
The undermentioned are transferred to the unemployed list:
2nd Lt. Robert Wilkinson. 13 Apr 1919."
I must say it's highly likely these are all the same man, and certain that he was still alive in April 1919.
Adrian