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I'd think the story is highly dubious, and is the sort of 'origin story' that many families concocted over many generations.
That said, James I of Scotland was forced to flee the country and took refuge on the Bass Rock in 1406, before attempting to seek safety in France. However I doubt there were goats on the Bass Rock. It's more famous for gannets.
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I just found this which is quite interesting; https://en.wiktionary.org/wiki/scrag
There's also possible that the names "Skrauke/Skruk/Skærauke" are traces of Skragge in Norway. ( http://www.disnorge.no/slektsforum/viewtopic.php?t=77590 )
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It seems most likely to me it would have been a local Sept leader, or at best a Earl or Laird, who got run out of his territories in the course of typical Scottish infighting. Over generations of retelling this guy could easily have been eventually promoted all the way to a "King", as it makes the family's origins sound more respectable. You would be positively amazed how many people in the USA claim descent from a Cherokee princess (the Cherokee don't even have royalty).
An event very much like this, known as the Flight of the Earls, happened in 1607. Another page I found talks of issues with "Scottish mercenaries" in Ireland prior to 1570. If we assume that Ireland wouldn't have been the only victim of this activity, your "king" could well have been one of those mercenary leaders.