We do not currently know of any antonyms for Flintshire.
The proper noun Flintshire is defined as:
A maritimetraditional county bounded to the north by the Irish Sea, to the northeast by the Dee estuary, to the east by Cheshire and to the south and southwest by Denbighshire. A detached part, Maelor Saesneg, is bounded on the northwest by Denbighshire, on the northeast by Cheshire, and on the south by Shropshire. There is a further small detached part around Marford.