WordNet records no synonym and no antonym for skivvies. It is the only member of its synset, 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.
(used in the plural) men's underwear consisting of cotton undershirt and underpants
Synonyms, antonyms and the broader and narrower relations for skivvies come from Princeton University’s WordNet. Full sources and licences.