My father in law remembers Kidwelly Flats, and says it was just west of the road overbridge that leads tot he entrance of the country park today. I'm not sure how far exactly his definition of just west would be, but he maintains it was between the RAF airfield and the Royal Ordnance Factory, and not really adjacent to either.
He recalls that he himself used to get a bus from Llanelli to the ROF, but that those form the west used a train to reach Kidwelly Flats, where they got on to a bus to be taken into the factory complex.
I don't doubt that the halt was created during wartime in order to provide better access to both RAF Pembrey and the weapons factory nearby.