Not only is a lamp cord unsuitable due to small gauge wire and non-heat resistant insulation, but it also lacks the rubber boot at the heel of the iron handle, which helps keep the cord from getting a sharp bend at the handle or getting under the hot sole plate. I can't tell for sure, but it looks like that iron simply has some electrical tape in lieu of a boot. Not good.
I remember once upon a time using an old iron with a frayed cloth cord. It shorted out at the handle, letting off sparks with a POP! and a nice blue flame. I was about 13 at the time and pretty shaken by the experience. As I recall the short didn't trip the circuit fuse (it was back in the day when we had glass fuses in the panel) but fortunately the short burned itself out and I was able to unplug the iron.