www.freereg.org.uk has some interesting burials in Chiilingham:
James Pringle, abode Wooler, buried 28 Jan 1814 aged 33
Also poss connected?
John Pringle buried 7 Nov 1813 aged 92, abode Wooler
I have often come across instances of families who were normally non-conformist (of the Protestant kind) baptising illegitimate children in a nearby Church of England parish rather than their usual church.
It does seem that this particular Pringle family has (or retained?) an association with Chillingham even though living in Wooler. As you can see from this map,
http://www.genuki.bpears.org.uk/NBL/nblmap.htmlChillingham is not strictly speaking contiguous with Wooler, but there is only a v small part of Chatton parish separating them.
There is also this Chillingham baptism:
Ann daughter of Ann Pringle, Spinster, abode Chillingham Barns, baptised 28 Feb 1830.
I will leave you to have a look at the rest on freereg - they are mainly later. The Chillingham data on freereg starts at 1812 & I could not see Chillingham amongst the BTs on familysearch, unless they are one of the ones that have been oddly indexed. Genus does refer to BTs being extant for Chillingham.
However, I do have a transcript of burials for Chillingham from 1692 to 1812 which has these burials:
William Pringel [sic] of Barns buried 26 April 1728
Isaac Pringle son of Jane buried 25 Dec 1729
Elizabeth Pringle daughter of John buried 7 August 1777
Isabel Pringle wife of George of Chillingham Park buried 8 Dec 1782
Isabel Pringle of Chillingham aged 67 buried 25 April 1797
Mary Pringle wife of John of Wooler died 19 May aged 62, buried 21 May 1809