No, they certainly do not have a copyright on the flags. They cannot stop anyone producing a very, very close imitation of their drawings. But following the blazon—emblazon argumentation, they may have a copyright on their particular rendering of a flag, even if the flag/blazon is PD. I think the issue is similar to maps: the geodata is PD as bare facts (well, for the time being at least), but a particular map drawn from that geodata is copyrighted. We may draw our own maps, but we cannot copy someone else's copyrighted map.

Besides, I take the liberty to not support either side here. As I wrote above; I did not tackle the issue until now, and I don't feel I know enough about the issue to give an opinion with confidence. I just think that it is well possible that they do have a copyright on their images.

Except maybe in the case of very simple designs (three differently colored stripes, for instance) where indeed a "no originality" claim might be valid. But for more complex flags, that argument breaks down. AFAIK, identical blazons have been rendered quite differently throughout history, e.g. with animals shown in a more "classical" or a more "modern" style. Take for instance Image:Kent Flag.gif. The blazon is "Gules a Horse forcene Argent". Now look at the COA shown there, at our flag, and at the renderings on the website of the Kent County Council... I think they all comply with that blazon, but are all different and IMO show enough creativity and originality to be individual copyrightable works.