Burning steel means burning Fe, not Fe3+. In the form of wool, steel powders have a very high surface area and as such the constituent metals burn in the presence of aerial oxygen to form most stable oxides of constituent elements. Steel is an alloy of iron with othe metals like chromium, manganese etc. a nonmetal carbon.
2Fe + 3O2 ->2Fe2O3, 2Cr + 3O2 -> 2Cr2O3, C + O2 -> CO2, 3Mn + 2O2 -> Mn3O4 etc.
A very bright flame resembling that of burning gunpowder is produced during such burning. In fact very fine iron powder was one of the components of primitive gun powders.