Hello and welcome to BYC! Glad you joined.
All areas of all towns and cities that are incorporated have zoning ordinances or deed restrictions in the property title that would be recorded with the governing authority.
People here can speculate all they want. Go to the governing authority and ask for a written copy of the applicable ordinance.
I've read the city ordinance, and it said only chickens and rabbits are allowed. It seems crazy that ducks would not be allowed in the City of Centennial. They seem the same to me...ducks, chickens.