WhatsApp isn't even open source, so no, it doesn't have reproducible builds. (Signal is open source and does have reproducible builds).
> Do we know that the app isn't storing the keys somewhere else?
No, but WhatsApp is still strictly better than either email or SMS. Even if you don't trust Facebook, that still only leaves three parties that can compromise the integrity of messages (you, the recipient, and Facebook), as opposed to the uncountable number of parties that can passively observe email or SMS in transit.
