Spectral domain phase microscopy (SDPM) is a function extension of spectral domain optical coherence tomography. SDPM achieves exquisite levels of phase stability by employing common-path interferometry. We discuss the theory and limitations of Doppler flow imaging using SDPM, demonstrate monitoring the thermal contraction of a glass sample with nanometer per second velocity sensitivity, and apply this technique to measurement of cytoplasmic streaming in an Amoeba proteus pseudopod. We observe reversal of cytoplasmic flow induced by extracellular CaCl2, and report results that suggest parabolic flow of cytoplasm in the A. proteus pseudopod.