... If the figures quoted by 'Bullshooter' are correct (I'm not disputing them) then the flame from an alcohol burner MAY be too hot for safety. Probably make less mess than a sooty candle or kerosene wick flame, though ....
Cartridge case annealing may result in unsafe cases if the case head is heated sufficiently to become soft. (Thus the precaution with some procedures of standing cases head down in a pan of water.)
The safety of the annealing process using a candle or other heat source is achieved principally by holding the case amidships with fingertips, and also by then promptly cooling the case with water when it's become too hot to hold without pain. Barker suggests the temperature at which pain occurs is about 150°F, and that the middle of the case reaches this temperature when the case neck reaches about 700°F in a candle flame.
The reason for the prompt cooling with wet towel or pan of water is not provided in Barker's article, as nearly as I can discover from about three read-throughs. I presume that prompt water cooling prevents the case head from becoming too hot. If the case were allowed to air cool, heat in the neck area might be conducted down the length of the case and soften the case head.
Barker cited with approval the case annealing technique described by William Dresser in
The American Rifleman (Sept 1962, p.42). Dresser using a propane torch to heat the case neck, holding the case with his fingertips. When a Tempilstik indicating crayon showed the neck had reached 700°F, the case was dropped immediately into a bucket of water.
A propane torch has a much hotter flame than a candle, and in that respect the Dresser method might resemble the use of an alcohol lamp. However, the important difference between the torch and candle methods is that neck temperature was evaluated directly with the torch. Neck temperature is judged indirectly with the candle technique using fingertips as heat sensors. Use of an alcohol lamp with crayon or lacquer indicator should be a safe and workable method.
--Bob