Though there seems to be some uncertainty over the precise spelling of the Cuinn name, you seem clear that he was married to a Jean/Jane Kincaid. (Jean and Jane are interchangeable names in Ireland and Scotland). If the couple married in Ireland you would expect them both to come from the same general area. You can use this site to see where surnames were most common in Ireland in the mid 1800s. Kincaid/Kincade was most common in Co Donegal and also found in Co. Derry. It wasn’t found in Mayo or Sligo though some of the clusters in southern Co Donegal are close to Sligo.
https://www.johngrenham.com/findasurname.php?surname=Kincaid
The timing of your ancestors’ migration in the early 1700s points to Presbyterian/Protestant ancestry. (Native Irish, who were RC, didn’t start migrating in large numbers till the 1800s but the Scotch-Irish, or Ulster-Scots as they are known in Ireland, started moving in significant numbers from about 1718 onwards). Presbyterian/Protestant points mainly to the counties of Ulster, such as Donegal and Derry, and in turn it points to Scottish ancestry, probably having settled in Ireland in the 1600s as part of the Plantation.
But that said, as Miriam has explained, there are very few records from that period and sadly you will probably struggle to find any documentary records of your ancestors in Ireland. But my feeling is the family may have come from Donegal, Derry or Tyrone.
If you are interested in why the Scotch-Irish left Ireland in such large numbers in the 1700s, this link gives a bit of background:
https://www.ancestryireland.com/wp-content/uploads/2017/08/The_1718_Migration.pdf
