If it is really slate, it could have come from many different places -- including North Pembrokeshire.
It is not beyond the bounds of possibility that it has indeed come from a glacial erratic.
Vespasian’s Camp: Cradle of StonehengeApril 19, 2013 By
Extract: "Most intriguingly, we also recovered a small worked slate point shaped like a microlith: the only prehistoric slate tool we know of ever discovered in the UK. By itself this would be interesting, but the fact it was found in a Mesolithic context just over a mile from Stonehenge makes it very significant. Tim Darvill says the slate is a kind of metamudstone, which would make the tool more durable. We are still trying to determine the provenance of the stone. There is no slate in the Stonehenge area – indeed, the nearest source we know of is in north Wales. It could have been fashioned from glacial erratic, though we are not aware of any such slate erratics in the vicinity. The alternative is that this points to a significant movement of people and ideas, pre-dating what went on at Stonehenge by thousands of years. All signs point to this site being regarded as a special place to gather."