The clan system was a social feature of the Highlands and Islands; not every Scot is or was a member of a clan. Arnot(t) is not a clan or Highland name. It originates as a territorial surname from the lands of Arnot in Kinross-shire, which is firmly in the Lowlands.
There may or may not be an Arnott tartan, but if your Arnotts were in Kintyre, they must have moved there from somewhere else.