The integration of color filters with microfluidics has attracted substantial attention in recent years, for on-chip absorption, fluorescence, or Raman analysis. We describe such tunable filters based on the micro-flow of liquid crystals. The filter operation is based on the wavelength-dependent liquid crystal birefringence that can be tuned by modifying the flow velocity field in the microchannel. The latter is possible both temporally and spatially by varying the inlet pressure and the channel geometry, respectively. We explored the use of these optofluidic filters for on-chip absorption spectroscopy in poly(dimethylsiloxane) microfluidic systems; by integrating the distance-dependent color filter with a dye-filled micro-channel, the absorption spectrum of a dye could be measured. Liquid crystal microflows substantially simplify the optofluidic integration, actuation and tuning of color filters for lab-on-a-chip spectroscopic applications.