Many trees claim this James belongs to John SINTON and Margaret LEARMONT/LARMENT of Ashkirk.
This John married Margaret in Dec 1735, immediately producing a Kathrine baptized the next month, and an Alexander the next year. The first gap in the known children is between 1740 and 1746, too late for this James
James father of Peter (estimated to be born about 1750/1752) and the James father of Thomas (born 1755) even if they are indeed the same James is unlikely to be born after 1730, assuming he was at least 20 before marrying.
There is a potential James Sintoune baptised in the Yarrow parish registers to a James Sintoune at Deloran (possibly modern day Deloraine in Kirkhope parish) that may be of interest, where West Deloraine Farm in Kirkhope parish features as a place some descendants are found in the the 19th century - bit of a stretch as "proof", but interesting nonetheless. Henderson-2297
Was James carrier at Abbotrule one and the same as James at Bairnkine?
Abbotrule baptisms exist for Thomas (1755), Margaret (1758) and James (1760) and Peter is assumed to fit in this family given he is estimated to have been born 1750/1752
Peter is the only one with subsequent records found to date.
The family of James married to Janet Oliver does not overlap by date, as the marriage is 1762. It does however contain both a Margaret (1765) and a James (1772), which if they are the same family, imply the first two of these names had died young.
BigY DNA matches from descendants from both Peter and the younger James show them as the same terminal SNP, haplogroup R-BY103089
Peter from the first family is described on certificates as "cattle dealer Burnkin", the place associated with the second 
We have BigY DNA results from three people believed to descend from James, they all share R-BY103089 (P312>R-DF27>R-ZZ12_1>R-BY70330>R-BY103089) where yFull currently estimates the time to MRCA at about 1750.
One a descendant of Peter, two others descendants of James, via respectively his sons James and Andrew.
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It may be possible to confirm family relationships with James by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: