As a teacher of German I have been called Nazi and Hitler by children who clearly know it's offensive and mean to be offensive. I would be amazed that Harry's extremely expensive and allegedly thorough education would have missed such a large part of our modern history.
Nazi-ism and the Holocaust are on the National Curriculum for Key Stage 3, though schools can choose whether to cover it or not.
At GCSE, which is no longer compulsory for History, it is covered by at least one exam board.
Whether Harry meant to be offensive or not is beside the point - he was offensive to many, many people. Either he was ignorant of the offence his costume would cause or he didn't care. Both options seem likely. He seems to require more education, but preferably not from the the Sun. Harry is an adult who is about to start training to lead others into life and death situations. What does his so-called sense of humour say about his ability to handle sensitive situations in Iraq, or Sudan or anywhere else troops might be sent?