Sorry, Lynn, but my Belfast friend and co-administrator of my Lynn Y-DNA project knows exactly how O'Flynn in many cases became O'Lynn. He said that, in the Irish, the "F" in "O'Flynn" is only faintly aspirated and sounds more like a breathy "H". Eventually, he continued, many O'Flynns simply stopped writing the "F".
I'm curious as to whether you know any males named O'Lynn who've had or would be willing to take a Y-DNA test. I have no doubt that some of them at least would have matches among O'Flynns.
In any case, Gaelic is a culture, not an ethnicity, and yes there is a lot of Gaelic influence in some parts of Scotland. However, Scotland also over many centuries had large influxes of English, French (including Normans), Dutch, and others. Being Scottish, therefore, also is not an ethnicity. It is a nationality. As to Lynns in Ulster ...
William and the other two Lynns who settled in Ulster during the first plantation - John and David - were from a landed family in Ayrshire, Scotland that had close ties with both the Hamiltons and the Boyds and were, by all accounts, Anglo-Norman and not Gaelic.