Let's see if I got that right, the birth registration of his son John Miller in Scotland in 1855, would that be because he was born in Scotland? I googled Kirkwall-Ireland and nothing but Kirkwall, Scotland yes.
It seems to be in the Orkney's (Scapa).
Regardless you can find parish records for 1855 on
www.rootsireland.ie you search with father
James and John the son and if there is one it would be there. Many parish records in Ireland were destroyed. Church of Ireland? or RC, most Scots in Ireland seem to be Methodists.
The name James Miller - and his birth in 1820 - James is the 2nd. most used forename in Ireland and there would be many of them.
In the Griffith Valuation for Ireland 1846-1864 there are 276 James Miller's.
Most Scots settled in the North of Ireland and were part of the original plantation of Scot's farmers to
Ireland "Plantation of Ulster".
www.askaboutireland.ie The North counties did not under go this valuation till the 1860's, where as the southern areas most in the 1840-50's.
Annette Code