The Flink sources include many examples for Flink’s different APIs:
These instructions explain how to run the examples.
There are also a few blog posts published online that discuss example applications:
How to build stateful streaming applications with Apache Flink presents an event-driven application implemented with the DataStream API and two SQL queries for streaming analytics.
Building real-time dashboard applications with Apache Flink, Elasticsearch, and Kibana is a blog post at elastic.co showing how to build a real-time dashboard solution for streaming data analytics using Apache Flink, Elasticsearch, and Kibana.
The Flink training website from data Artisans has a number of examples. Check out the hands-on sections and the exercises.