Measuring gas and liquid flow rate is paramount in various scientific and industrial applications. This work presents an optical fiber flowmeter based on a graphene oxide (GO) coated Michelson interferometer. The interferometer is fabricated using a long-period fiber grating (LPFG) followed by a GO-coated single-mode fiber (SMF). By radiating the GO coating, it experiences photothermic effect that induces local heating of the film. This results in a variation in the effective refractive index in the cladding modes, which induces a phase shift on the interferometer spectrum. When a gas flow is introduced near the coated fiber, the “hot-wire” region will experience a reduction in temperature proportional to the flow rate. The flowmeter exhibited a linear wavelength shift to the flow rate with an absolute sensitivity of 17.4 ± 0.8 pm/(L.min-1) for gas flow rates between 2 and 8 L/min. Furthermore, the dynamic response of the sensor was studied, attaining a maximum response time of 1.1 ± 0.4 s