We design and demonstrate a compact, robust, and simple to assemble and tune permanent magnet suitable for NMR relaxometry measurements of microfluidic flows. Soft-magnetic stainless-steel plates, incorporated inside the magnet airgap, are key for obtaining substantially improved and tunable field homogeneity. The design is scalable for different NMR probe sizes with the region of suitable field homogeneity, less than 200 ppm, achievable in a capillary length of about 50 % of the total magnet length. The built physical prototype, having 3.5x3.5x8.0 cm3 in size and 5 mm high airgap, provides a field strength of 0.5 T and sufficient field homogeneity for NMR relaxometry measurements in capillaries up to 1.6 mm i.d. and 20 mm long. The magnet was used for test flow rate measurements in a wide range, from 0.001 ml/min to 20 ml/min.