I found all sorts of references to the Lt Col John Kay who was in the 12th regiment of foot, but I have nothing at all to indicate that this could be the same person who was the father of Sophia.
He must have enlisted in the army around 1756 and eventually rose to the rank of Lieutenant-Colonel in the 12th Regiment of Foot. He was wounded at the battle of Minden in 1759 and was commended in some way.
Wounding at Minden:
https://archive.org/stream/recordoftwentyfi00canniala/recordoftwentyfi00canniala_djvu.txtPromotion to Lieutenant:
http://search.findmypast.co.uk/bna/ViewArticle?id=BL%2F0000545%2F17680801%2F015%2F0055&browse=truePromotion to Brevet Major:
http://search.findmypast.co.uk/bna/viewarticle?id=bl%2f0000554%2f17801127%2f016Promotion to Major:
http://search.findmypast.co.uk/bna/viewarticle?id=bl%2f0000045%2f17860621%2f003Discussion of his acquiring Glenboig:
https://archive.org/stream/strathendrickits00smit/strathendrickits00smit_djvu.txtMIDDLE GLENBOIG alias GLENBOIG CUNNINGHAME.
"... The successive proprietors of Elizabeth Adam's half were John Buchanan, her son, and Andrew Buchanan, her grandson; the latter sold it to Peter Spiers in 1792, and he almost immediately disposed of it to Lieut.-Colonel John Kay. Margaret Adam's half was, in 1723, in possession of John Adam, who, by his wife, Margaret Kay, had at least three sons : Robert, Alexander, and Andrew,
and a daughter, Helen, born in 1 728.2 They seem to have sold their share of it to William Kay; and his son, Lieut.-Colonel John Kay, was the next proprietor, and Middle Glenboig became reunited in him. In 1795 the Colonel disponed the property in favour of his nephew, Alexander Ure, merchant in Glasgow;"
I cannot find evidence of John Kay being stationed in Blandford, Dorset, in the 1770s, but there was a military camp there at the time, so it is not unlikely that if he had a daughter she might have come to know the son of local gentleman James Knight snr.
It's distinctly possible that the Fintry, Bermondsey and Blandford John Kay's are either all the same person or three different ones. Nothing to link any of them together except the names.