The Army Rifle Association Meeting took place from 8th July 1909 and lasted three days, with the Roupell Cup and the Revolver Twenty on the final day. The Roupell cup, according to the Times, was designed for those who were debarred from taking part in the Army Championship, and consisted of 7 rounds at 300, 600, and 800 yards, and the other conditions the same as for the King's Prize.
The scores were:
1. Armourer Staff Sgt Brown, AOC, 95.
2. Captain Mayne, late Royal Inniskilling Fusiliers, 94
3. Sergeant-Major Wallingford, School of Musketry, 94
4. Q.M.S.I. Bostock, School of Musketry, 94
5. Captain McVittie, AOD, 93.
6. Captain Henderson, Indian Army, 93.
7. C.S.I.M Armston, Leicester Regt, 93
8. Colonel McDonald, Indian Army, 93
It goes on to say that a feature of this competition was the excellent shooting of the AOC, particularly seeing as it was only recently, due to the efforts of Captain McVittie, that their interest has been turned to rifle shooting.
For the military record at the National Archives - this depends very much on when he was discharged, do you know? If he was still with the army in 1920 his record will still be at the MOD.
www.nationalarchives.gov.uk/documentsonline - you can look to see if he got WWI medals at all, there are several Browns with the rank of 'Armourer Staff Serjeant' in the AOC: W.E, John J, James, another James, Frederick C, Charles B, and Albert E. If one of these is yours that will help because it will give you his regimental number.
If you can't find him at all in the WWI medal rolls, or you know he left the army before WWI, then there are indexes to discharge records from 1900-1913 at the NA you should look at. If he was discharged during or just after WWI, it gets a bit more difficult and you should ask someone at the NA for help - these are the so-called 'burnt records' and it definitely helps to have an expert opinion!