In this paper, we present a miniature fluidic flow sensor based on a short fiber Bragg grating inscribed in a single mode fiber and heated by Co2+-doped multimode fibers. The proposed flow sensor was employed to measure the flow rates of oil and water, showing good sensitivity of 0.339 nm/(m/s) and 0.578 nm/(m/s) for water and oil, flowing at v = 0.2 m/s. The sensitivity can be increased with higher laser power launched to the Co2+-doped multimode fibers. A small flow rate of 0.005 m/s and 0.002 m/s can be distinguished for a particular phase of water or oil, respectively, at a certain laser power (i.e. ~1.43W). The flow sensor can measure volume speed up to 30 L/min, which is limited by the test rig. The experimental results show that the sensor can discriminate slight variation of flow rates as small as 0.002m/s.