Your Bible is shelved by kind — law, history, poetry, prophecy — not by date. This plan puts it back in the order events happened.
So Job sits with the patriarchs, each prophet arrives in the reign he actually preached in, and Paul's letters land inside the journeys of Acts, at the point in the story where he wrote them. The Psalms come in at the eras their five books belong to.
Two things this plan will not do: it never cuts a chapter in half, and it does not splice the four Gospels into one merged account — where those four should be interleaved is a real argument among scholars, and a reading plan is no place to settle it quietly. You read each Gospel whole.