I have done a bit more searching on the subject of the Senior Officers' School Sheerness. It would appear that it was a very important establishment from which all senior army officers who aspired to higher army commands had to qualify. Established on a permanant peacetime footing in 1920-21, the school had two branches, one at Sheerness and the other at Belgaum, India.
From looking through various records that have come to light it would appear that the school at Sheerness wasn't confined to just British army officers. Officers aspiring to higher commands in the RN and RAF attended courses at Sheerness concerned with tri-service co-operation. I have also found evidence from various papers held at the IWM and in the Liddel Hart Archive that officers destined for higher command in the Canadian, South African, and ANZAC forces also attended the Sheerness School. Many of those who attended at Sheerness can be found occupying senior posts of the British and Empire Forces during WW2 and Korea.
A few of the personalities I have found linked to the school are:
The Viscount Gort VC. 1846-1946. CIGS 1937 and CinC BEF 1939/40.
General Sir John Northcott. 1890-1966. Australian Imperial Force. Governor of Australia 1951 and 1956.
Major General Evered Poole CB. 1902-1969. GOC 6th South African Armoured Div 1944/45. Deputy Chief of the General Staff South African Army 1946.
Admiral of the Fleet Sir Andrew Cunningham. 1883-1963.
Major General D N Wimberley. 1896-1983. Director of Infantry at WO 1944-46.
Squadron Leader H W Evans RAF.
Vice-Admiral R Hallifax. 1885-1943.
Lt-Gen Sir Wilfred Lindsell RA 1884-1973. Lectured at Sheerness on 27th Feb 1927 on tanks and inter-arm co-operation.
The list of tri-service and Empire officers who trained at or taught at the school is quite extensive.
It would appear that the Senior Officers' School Sheerness could be compared to the present day Royal College of Defence Studies. The only clue I have to its location is gleaned from Hansard December 3rd 1930 in which the SofS for War stated that "The Senior Officers' School is now accommodated in Sheerness barracks". However it is listed as being located at Sheerness from its establishment in 1920, so where it was before the SofS's 1930 statement is a mystery to me.