A quick google search turns up definitions of "kinch" as a word for a noose or loop in a rope, and also as slang for "an unfair advantage". (online dictionaries and etymology sites, an excerpt from a book called "Death of a Joyce Scholar"). Whether it's a coincidental homophone or maybe separate lines of Kinches got their names in different ways, my older relatives were quite fond of this bit of trivia.
I don't know how accurate family legend is, but given my ancestor's boasts of how they treated the Catholics, and that they didn't see themselves as Irish even after being there for 200 years, it seems believable that they would have reason to flee...
I also don't know how big an "uprising" we're talking. It could have just been 1 angry mob, or ongoing Catholic/Protestant hostilities