WordNet records no synonym and no antonym for stampede. 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.
act, usually en masse, hurriedly or on an impulse
“Companies will now stampede to release their latest software”
a headlong rush of people on a common impulse
“when he shouted `fire' there was a stampede to the exits”
a wild headlong rush of frightened animals (horses or cattle)
2 of the 6 recorded senses carry no synonym, antonym or related term, so they are not shown above. Every sense, with its definition and examples, is on the full entry for stampede.
Synonyms, antonyms and the broader and narrower relations for stampede come from Princeton University’s WordNet. Full sources and licences.