The process described is called rusting. Rusting occurs when iron reacts with oxygen and moisture (water vapor) in the air. The reddish-brown flaky substance formed is hydrated iron(III) oxide ($Fe_2O_3.xH_2O$), commonly known as rust. This is a slow oxidation process. Burning involves rapid combustion and significant heat, which is not what happens here. Evaporation and sublimation are physical changes, not chemical reactions that form new substances like rust. Iron hydroxide and carbonate are not the primary products of typical iron rusting.