How was the Kansas-Nebraska Act supposed to help slavery?

It was not meant to 'help slavery'. It was meant to provide a peaceful solution to the slave-controversy on the admission of each new state to the Union, by letting the locals vote on it.

In fact, it had the opposite effect. When Kansas became the first state to vote, all the bully-boys from both sides rushed to Kansas in order to intimidate the voters, and it became 'Bleeding Kansas'.