WordNet records no synonym and no antonym for burner. 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 apparatus for burning fuel (or refuse)
“a diesel engine is an oil burner”
the heating elements of a stove or range on which pots and pans are placed for cooking
“the electric range had one large burner and three smaller one”
Synonyms, antonyms and the broader and narrower relations for burner come from Princeton University’s WordNet. Full sources and licences.