We demonstrate an imaging system employing continuous high-rate photonically-enabled compressed sensing (CHiRP-CS) to enable efficient microscopic imaging of rapidly moving objects with only a few percent of the samples traditionally required for Nyquist sampling. Ultrahigh-rate spectral shaping is achieved through chirp processing of broadband laser pulses and permits ultrafast structured illumination of the object flow. Image reconstructions of high-speed microscopic flows are demonstrated at effective rates up to 39.6 Gigapixel/sec from a 720-MHz sampling rate.