Microfluidic laboratories-on-a-chip (LoCs) are replacing the conventional biochemical analyzers and are able to integrate the necessary functions for biochemical analysis on-chip. There are several types of LoCs, each having its advantages and limitations. In this paper we are interested in flow-based LoCs, in which a continuous flow of liquid is manipulated using integrated microvalves. By combining several microvalves, more complex units, such as micropumps, switches, mixers, and multiplexers, can be built. We consider that the architecture of the LoC is given, and we are interested in synthesizing an implementation, consisting of the binding of operations in the application to the functional units of the architecture, the scheduling of operations and the routing and scheduling of the fluid flows, such that the application completion time is minimized. To solve this problem, we propose a list scheduling-based application mapping (LSAM) framework and evaluate it by using real-life as well as synthetic benchmarks. When biochemical applications contain fluids that may adsorb on the substrate on which they are transported, the solution is to use rinsing operations for contamination avoidance. Hence, we also propose a rinsing heuristic, which has been integrated in the LSAM framework.