Converting AlCl3 to Al2O3
Yes, you can make aluminium oxide from aluminium chloride pretty much in your way but then again as @andselisk said, it is a pretty inefficient reaction and wastes a lot of fuel and energy and also produces many byproducts. Hence, the reaction is the other way round if considered on an industrial scale. The main preparation method is already described by @andselisk in the comment section. Only to verify its authenticity, here is a patent claim:


  A process for preparing alumina which comprises heating aluminum
  chloride hexahydrate at a temperature of from about 225 to 600 F. For
  a period of time such as to liberate only a portion of its chlorine
  content, commingling a basic reagent with the resultant
  chlorine-containing residue to form aluminum hydroxide, washing and
  filtering the latter and then calcining to produce the oxide.