When I started searching I found about 70 families in the USA but most had Irish links. My links go back to Scotland, to Newton Stuart. The question is did the name come from Ireland or is it a Scottish name. There are few Kinnas left in the UK now although McKinna is more common. During a trip to Newton Stuart in the 60's I spoke to a lady who said it was common for the McKinna's, going south to England, to drop the Mc. As an example my gggggrandfather, William b1773, came down to London to work, he married and had their first child in London, his father was William McKinna of New Galloway.
I observe, from G. F. Black's authoritative work ?The Surnames of Scotland" that the name Kenna., Kenney, Kinna comes from MacKenna and its variants (Gaelic MacCionaodah, son ofCionaodh.It is a Galwegian surname, and appears in Scottish records as early as 1473 (in Wigtown). Wigtown, just a few miles down the road from Newton Stewart, was an important port in the days of sail.