flag has 13 distinct synonyms spread across 7 of its 12 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
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.
emblem usually consisting of a rectangular piece of cloth of distinctive design
plants with sword-shaped leaves and erect stalks bearing bright-colored flowers composed of three petals and three drooping sepals
a rectangular piece of fabric used as a signalling device
flagpole used to mark the position of the hole on a golf green
stratified stone that splits into pieces suitable as paving stones
Synonyms, antonyms and the broader and narrower relations for flag come from Princeton University’s WordNet. Full sources and licences.