"Anthrax" (coal) and "anthros" (a flower) look very similar, but I don't know if there's any connection.

It's anthos for flower, Hib., as in anthology (whose Latin calque is florilegium). According to Pokorny, it's from the PIE root *andh- 'to stand out, jut out; to flower, bloom'. You might have been thinking of Greek antheros 'blooming' which is from the same root, which also gives Middle Irish ainder, aindir 'young woman', Welsh anner 'young cow', Old Welsh enderic 'vitulus, veal', Welsh enderig 'bull, ox, bullock', Breton ounner 'young cow'. Cool, but supposedly not related to anthraks.