John and Margaret baptized 5 children in Kendal. Their surname had multiple spellings: Margaret BARNS/BARNIS (the two transcripts differ), Elizabeth BARNISSE and William, Elizabeth and Ann BARNISH. Perhaps during this time the pronunciation of their name shifted from BARNISSE towards BARNISH as used by later generations.
John would have been born 1680-1690 so it is possible that John was the child of a Huguenot family who had fled France or the Spanish Netherlands following the Revocation of the Edit of Nantes in 1685.
Flemish protestant cloth-workers had moved to England and Ireland in the 14th century and had special districts assigned to them, with special liberties and privileges. They were planted all over England - in London, in Kent, in Somerset, in Norfolk, in Nottinghamshire, in Yorkshire, in Lancashire, and as far north as Kendal in Westmoreland
Looking for BARNIS(SE) records in France in 1650-1700 yielded just three - all from the Dordogne, a hotbed of Huguenot resistance. For example, the two below are just 30 miles apart
- Jaques BARNISSE, b 23 Feb 1671, Saint-Germain-du-Salembre, Dordogne, Aquitaine by Pierre BERNISSE and Toinie LABER
- Jeanne BARNISSE 1669-1749, buried in Razac-de-Saussugnac, Dordogne, Aquitaine
There are also BARNIESEs in Aisne departement in eastern France in the early 1700's.
Another explanation for the family's arrival is that he was from Scotland; Barnis is a Scottish placename. For example, in 1631 a John BARNIS, merchant, was elected Dean of Guild, in 1632 as bailey, and again in 1634 and 1635 as Dean of Guild, and later that year to commissioner to the particular of burghs being held in Edinburgh that year.
An IGI record of the death of a John BARNISH who was buried on 6 Apr 1726 in "Cumbria" has an alternative transcription of Jos BARNISH buried in Kendal (also from Family Search). As such it can be discounted.