flatness has 11 distinct synonyms spread across 3 of its 5 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.
the property of having two dimensions
a want of animation or brilliance
“the almost self-conscious flatness of Hemingway's style”
a deficiency in flavor
“it needed lemon juice to sharpen the flatness of the dried lentils”
the property of having little or no contrast; lacking highlights or gloss
inactivity; showing an unusual lack of energy
“the general appearance of sluggishness alarmed his friends”
Synonyms, antonyms and the broader and narrower relations for flatness come from Princeton University’s WordNet. Full sources and licences.