Learn Swedish: Chefen viskade att han visste hemligheten. - The boss whispered that he knew the secret.

This is an example of backshifting in indirect speech. Because the main verb viskade (whispered) is in the past tense, the verb in the att-clause (that-clause) also shifts to the past tense (visste) to match it, even if the fact of knowing the secret is still true right now.

Could I use kände instead of visste for knew?

No, because Swedish uses different words for knowing. You use veta (past tense: visste) for knowing facts or information, like a secret. You use känna (past tense: kände) for knowing people or places, like being familiar with a person.

Where would I put inte if he whispered that he didn't know the secret?

It would go right before the verb: ...att han inte visste hemligheten. Remember that in subordinate clauses (like the one starting with att here), sentence adverbs like inte are placed before the verb instead of after it.

How is the ch in chefen pronounced?

It is pronounced with the Swedish sj-sound, which often sounds similar to a soft English sh. Words borrowed from French that start with ch, like chef or choklad, usually use this sound instead of the hard English ch.