flutter has 20 distinct synonyms spread across 7 of its 9 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.
move along rapidly and lightly; skim or dart
“The hummingbird flitted among the branches”
flap the wings rapidly or fly with flapping movements
“The seagulls fluttered overhead”
abnormally rapid beating of the auricles of the heart (especially in a regular rhythm); can result in heart block
a disorderly outburst or tumult
“they were amazed by the furious disturbance they had caused”
Synonyms, antonyms and the broader and narrower relations for flutter come from Princeton University’s WordNet. Full sources and licences.