I learned from these wiki pages that acetone can be produced from calcium acetate, which can be produced by the reaction of eggshells and vinegar. However, I couldn't find the required temperature. Would it be possible to produce acetone vapours by simply heating calcium acetate over a natural gas flame (~1500 degrees C)?
Calcium acetate decomposes starting at around 160 degrees Celsius, according to Wikipedia. So yes, it is definitely possible to do so in a gas flame.