The pervasive availability of streaming data is driving interest in distributed Fast Data platforms for streaming applications. Such latency-sensitive applications need to respond to dynamism in the input rates and task behavior using scale-in and -out on elastic Cloud resources. Platforms like Apache Storm do not provide robust capabilities for responding to such dynamism and for rapid task migration across VMs. We propose several dataflow checkpoint and migration approaches that allow a running streaming dataflow to migrate, without any loss of in-flight messages or their internal tasks states, while reducing the time to recover and stabilize. We implement and evaluate these migration strategies on Apache Storm using micro and application dataflows for scaling in and out on up to 2-21 Azure VMs. Our results show that we can migrate dataflows of large sizes within 50 sec, in comparison to Storm's default approach that takes over $100~sec$. We also find that our approaches stabilize the application much earlier and there is no failure and re-processing of messages.