Learn Dutch: Mijn sleutels zijn spoorloos.

It literally means "without a trace." It is formed by combining the noun spoor (trace, track, or trail) with the suffix -loos (-less). It is a very natural and slightly dramatic way to express that an object or person has completely vanished.

Could I use the word kwijt to say my keys are missing?

Yes, but the grammatical structure would have to change. Kwijt is typically paired with the person who lost the item, using the verb zijn. You would say Ik ben mijn sleutels kwijt (I have lost my keys / I am missing my keys). You generally avoid saying Mijn sleutels zijn kwijt. Using spoorloos allows you to make the keys the subject of the sentence.

Why can't I use the verb ontbreken (to be missing) for this sentence?

Ontbreken is used when a necessary part is absent from a whole, or when something expected is lacking (such as a missing page in a book, or missing ingredients). For everyday misplaced personal items like keys or a phone, ontbreken sounds unnatural. Spoorloos or kwijt are the correct choices here.