Microfluidic biochips are replacing the conventional biochemical analyzers and are able to integrate the necessary functions for biochemical analysis on-chip. There are several types of microfluidic biochips, each having its advantages and limitations. In this paper we are interested in flow-based biochips, in which the 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. Although researchers have proposed significant work on the system-level synthesis of droplet-based biochips, which manipulate droplets on a two-dimensional array of electrodes, no research on system-level synthesis of flow-based biochips has been reported so far. The focus has been on application modeling and component-level simulation. Therefore, for the first time to our knowledge, we propose a system-level modeling and synthesis approach for flow-based biochips. We have developed a topology graph-based model of the biochip architecture, and we have used a sequencing graph to model the biochemical applications. We consider that the architecture of the biochip is given, and we are interested to synthesize 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. We propose a List Scheduling-based heuristic for solving this problem. The proposed heuristic has been evaluated using two real-life case studies and a set of four synthetic benchmarks.