What changes the cleaning answer
Do not burn candles in the same airspace as pet birds. This includes scented candles, wax melts, incense, and fragrance warmers.
Bird airways are sensitive
Birds breathe differently from mammals and can be affected by fumes that people barely notice.
Scent is not harmless
Fragrance oils, smoke, soot, and heated wax additives are unnecessary risks in a bird home.
Control the room air
Keep bird rooms fragrance-free, smoke-free, and away from cooking fumes, aerosols, and strong cleaners.
Better option
Use battery LED candles if you want the look without changing the air.