Depending on the size of the dataset you're talking about, and of the volume of the stream, I'd try to cache the database as much as possible (assuming it doesn't change that often). Augmenting data by querying a database on every record is very expensive in terms of latency and performance.
The way I've done this before is instantiating a thread whose only task is to maintain a fresh local cache (usually a ConcurrentHashMap), and make that available to the process that requires it. In this case, you'll probably want to create a processor, give it the reference to the ConcurrentHashMap described above, and when the Kafka record comes in, lookup the data with the key, augment the record, and send it to either a Sink processor, or to another Streams processor, depending on what you want do with it.
In case the lookup fails, you can fallback to actually do a query on demand to the database, but you probably want to test and profile this, because in the worst case scenario of 100% cache misses, you're going to be querying the database a lot.