In 1935 the Carmarthenshire County Council received a formal award of arms
which combined two Welsh dragons with two gold lions on a quarted red and gold, counter charged field, the quarters being divided by an an indented line. The lion and indentation are from the arms of Rhys ap Tewdwr Mawr, King of Deheubarth,
a kingdom occupying the territory of modern day Carmarthenshire, in the eleventh century; an armorial banner formed from these arms has been proposed as an appropriate flag for the modern county, which occupies the territory of the ancient kingdom.
These arms also made a decorative appearance at the 1969 Investiture of Prince Charles at Caernarfon Castle
The erstwhile administration of Dyfed included the Deheubarth arms to signify the inclusion of Carmarthenshire as part of its territorial remit
so there is certainly a precedent for use of this design to represent the county, indeed the flag is flown in the county today, as seen here in flight over Carmarthen Castle
The flag can be purchased here and here.