The answer is no, German is not commonly spoken in Uherský Brod. Uherský Brod is a town in the Czech Republic, and the official language of the Czech Republic is Czech. German is spoken by a minority of the population in some parts of the Czech Republic, but Uherský Brod is not one of those areas.
The Ultimate Uherský Brod Quiz: Test Your Knowledge of this Charming Czech Town!