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There were only 2 John Phillips records in the Griffiths. The one in Kilbarron parish The one in Inishkeel parish is a possibility since Inishkeel is just to the north of Killybegs Lower parish and many times emigrants said they were from the nearest big town (in this case Ardara).
This Irish Times web site http://www.irishtimes.com/ancestor/surname/ will show you where surnames were found in the mid-19th century based on the griffiths and also provides some background on the origins of the name. I don't think there is a Spanish Armada connection but anything is possible. I also have Phillips ancestors from East Co. Mayo and I've not heard anything about a Spanish connection.
Sometime this year, the land revision books will be online. These books show who took over properties after the Griffiths. maybe when these records are released you can track the John Phillips property in Inishkeel to see if you see any connections.