Mux has been using Apache Flink for stream-processing applications since 2016 and has learned valuable lessons from running it in Kubernetes clusters. They recommend one job per Flink cluster, using the official Flink Docker image, adding custom Prometheus metrics to applications, disabling DNS caching, and utilizing the new Flink memory management model. Future improvements include automated application upgrades with CI/CD and better test coverage for their Flink applications.