Continuous-flow microfluidic biochips (CFMBs) automatically execute various bioassays by precisely controlling the transport of fluid samples, which is driven by pressure delivered through fluidic ports. High-level synthesis, as an important stage in the design flow of CFMBs, generates binding and scheduling solutions whose quality directly affects the efficiency of the execution of bioassays. Existing high-level synthesis methods perform numerous transport tasks concurrently to increase efficiency. However, fluidic ports cannot be shared between concurrently executing transport tasks, resulting in a large number of fluidic ports introduced by existing methods. Increasing the number of fluidic ports undermines the integration, reduces the reliability, and increases the manufacturing cost. In this paper, we propose a port-driven high-level synthesis method based on integer linear programming (ILP) called SlimPort, integrating the optimization of fluidic port number into high-level synthesis, which has never been considered in prior work. Meanwhile, to ensure bioassay correctness, volume management between devices with a non-fixed input/output ratio is realized. Additionally, two acceleration strategies for ILP, scheduling constraint reduction and upper boundary estimation of fluidic port number, are proposed to improve the efficiency of SlimPort. Experimental results from multiple benchmarks demonstrate that SlimPort leads to high assay execution efficiency and a low number of fluidic ports.