There are two other births who look like the brothers of Bertie Philip Skillicorn:

20727/1877: SKILLICORN, PERCY A, [father]: PHILIP A, [mother]: SARAH, [place]: SOFALA .

8173/1883: SKILLICORN, CLAUDE WILLIAM, [father]: PHILIP, [mother]: SARAH, [place]: RANDWICK.
Claude's death appears on the index in 1945. The cert will show marriage, and his children's names and ages.

By the way, in that WW II Nominal Roll, both your Raymond Skillicorn [date of birth 24 Mar 1914] and Peter Philip Aubery SKILLICORN [date of birth 17 Nov 1922] give their next of Kin as Lucy Skillicorn. And Kenneth William [dob 25 Jun 1926] has Claude William as next of kin. See http://www.ww2roll.gov.au/

Sue