Many Orkney families around that time belonged to the Free Church or Baptist congregations - and few of those records have survived, only the Established church ones are almost complete. I have two families in Eday, with the one of the parents in each family who are siblings - all one family's baptisms are there - but none of the other family!
All I can see in the Orkney Family History Society indexes for your family are:
Death of John McKinlay, 1911, South Leith aged 69
John McKinlay died on 04/11/1911 at South Leith aged 69. Spouse of Barbara Simison.
Father: Hugh McKinlay. Mother: Janet Cockburn.
Informant: George McKinlay (Son)
[Death Cert: 1911-692-02-0728]
Death of Annie McKinlay, 1922 in Thurso, Caithness aged 85
Annie McKinlay died on 23/10/1922 aged 85 in Thurso.
Father: Hugh McInlay. Mother: Janet Cockburn
Informant: Alice Latimer, Grand Daughter
[Death Cert: 1922-041-00-0066]