there's no "job" for Kafka Streams, unlike cluster-based frameworks such as Spark or Storm, for which you typically can only use a limited set of monitoring tools. Instead -- and that is a great benefit -- you write standard Java (or Scala, ...) applications when using Kafka's Streams API, and you can monitor this application with any of the many, many tools that can manage and monitor a Java application.
On top of that, there are many built-in metrics that are exposed by the Streams API (e.g. via JMX or programmatically) that provide you with additional insights into your application.
-Michael