Your associate dean is a worthless sack of worm meat with no talent who couldn't cut it as a researcher or educator. Apply anyway. Keep a record, noting time and date, or every interaction with him and other administrators. If possible (and legal in your state) record those conversations/interactions. You could win the litigation lottery if he is as abusive as he seems.

More importantly, talk to your peers and chair and listen to their evaluations of your abilities. Get their feedback on how you would fit this new position. If they are positive, apply.

Just reading this situation makes me livid (and my now-former dean referred to me in racist language). Burn your associate dean down. Deans have a shelf life of ~five years before a university gets tired of their BS and kicks them to another institution (rarely promoting them in-house). Unless you really are an inferior engineer, you deserve the opportunity for the position, and not to be a servant beholding to the dean's new pet. If you accept this kind of treatment, it only perpetuates it to others.