WordNet records no synonym and no antonym for spread eagle. 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.
an emblem (an eagle with wings and legs spread) on the obverse of the Great Seal of the United States
a skating figure executed with the skates heel to heel in a straight line
Synonyms, antonyms and the broader and narrower relations for spread eagle come from Princeton University’s WordNet. Full sources and licences.