This is an alternative way of saying this is English and should be accepted.
Note: Another way of saying Have you got a brown jacket? in Ukrainian is Ви отримали коричневу куртку?
The phrase У вас є seems to be the more common way of asking this type of question.
If you were asking in a store, then using куртка would get you a jacket. They wouldn't show you a long coat, for instance, or any other type of coat. So I don't think coat is an acceptable translation as it is too generic.