But everything is wrong with this. First, a curious researcher (see web link below) burned a control pair of candles by themselves, without putting them in an ear, and found they contained the same orange residue. This is because the residue found inside used ear candles is from the candles themselves, not from your ear.
Second, candle heat can potentially create a weak convection current, but that's not a vacuum. Hold a burning ear candle near any sort of debris, like dust on a desk or salt on your kitchen bench, and you'll see that nothing is moved at all. Ear candles have no physical potential to perform their only advertised function.
Third, they're quite dangerous. Injuries from hot wax dripping into the ear canal are frequent. Equally common are burns suffered by people trying to hold their own ear candles.
Finally, your ear secretes wax for a reason. It guards against infections in the ear canal and removes dirt and other contaminants as it naturally flows outward. If for some reason you ever do get a problematic blockage of ear wax, it can be easily and safely removed with a bulb syringe or ear drops. There's never any reason to perform ear candling, which is proven to be both dangerous and useless.
Thanks to Brian for the article and Bobby Nelson for the photo.