Michiko talks as though she herself had been to the North Pole.

Literal

Michiko [topic-は] as-if herself North-Pole [to-へ] going came [whether-かのような] way-of-speaking [copula-だ].

かのような is a more literary simile marker than just ような — 'as though/as if.' 自分自身が emphasizes 'she herself.' 口ぶり means 'way of speaking/tone.'