Princess Diana plotted to move to South Africa with her lover Dr. Hasnat Khan in a bid to flee her “petulant” ex-husband, King Charles, her brother Charles Spencer claims in a bombshell new book. The tragic royal went as far as to speak to famed medical pioneer Dr. Christian Barnard as she hoped he could snag Khan, a British-Pakistani cardiothoracic surgeon, a post at his Cape Town hospital. As Spencer, her youngest sibling, notes in his new memoir, “Swan Song: My Sister, Diana,” out today, his sister was “prone to naive yet impossible dreams about as to how her life could be.” He details the chaos Diana lived in — a state of frenzy also…