WordNet records no synonym and no antonym for flax. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
fiber of the flax plant that is made into thread and woven into linen fabric
plant of the genus Linum that is cultivated for its seeds and for the fibers of its stem
Synonyms, antonyms and the broader and narrower relations for flax come from Princeton University’s WordNet. Full sources and licences.