We introduce FlowFlex, a highly generic and effective scheduler for flows of MapReduce jobs connected by precedence constraints. Such a flow can result, for example, from a single user-level Pig, Hive or Jaql query. Each flow is associated with an arbitrary function describing the cost incurred in completing the flow at a particular time. The overall objective is to minimize either the total cost (minisum) or the maximum cost (minimax) of the flows. Our contributions are both theoretical and practical. Theoretically, we advance the state of the art in malleable parallel scheduling with precedence constraints. We employ resource augmentation analysis to provide bicriteria approximation algorithms for both minisum and minimax objective functions. As corollaries, we obtain approximation algorithms for total weighted completion time (and thus average completion time and average stretch), and for maximum weighted completion time (and thus makespan and maximum stretch). Practically, the average case performance of the FlowFlex scheduler is excellent, significantly better than other approaches. Specifically, we demonstrate via extensive experiments the overall performance of FlowFlex relative to optimal and also relative to other, standard MapReduce scheduling schemes. All told, FlowFlex dramatically extends the capabilities of the earlier Flex scheduler for singleton MapReduce jobs while simultaneously providing a solid theoretical foundation for both.