Cells can localize molecules asymmetrically through the combined action of cytoplasmic streaming, which circulates their fluid contents, and specific anchoring mechanisms. Streaming also contributes to the distribution of nutrients and organelles such as chloroplasts in plants, the asymmetric position of the meiotic spindle in mammalian embryos, and the developmental potential of the zygote, yet little is known quantitatively about the relationship between streaming and the motor activity which drives it. Here we use Particle Image Velocimetry to quantify the statistical properties of Kinesin-dependent streaming during mid-oogenesis in Drosophila . We find that streaming can be used to detect subtle changes in Kinesin activity and that the flows reflect the architecture of the microtubule cytoskeleton. Furthermore, based on characterization of the rheology of the cytoplasm in vivo, we establish estimates of the number of Kinesins required to drive the observed streaming. Using this in vivo data as the basis of a model for transport, we suggest that the disordered character of transport at mid-oogenesis, as revealed by streaming, is an important component of the localization dynamics of the body plan determinant oskar mRNA.