Effective water resources management depends on monitoring the volume of water flowing through streams and rivers, but collecting continuous discharge measurements using traditional streamflow gauges is prohibitively expensive. Time-lapse cameras offer a lowcost option for streamflow monitoring, but training models for predicting streamflow directly from images requires streamflow data to use as labels, which are often unavailable. We address this data gap by proposing the alternative task of Streamflow Rank Estimation (SRE), in which the goal is to predict relative measures of streamflow such as percentile rank rather than absolute flow. In particular, we use a learning-to-rank framework to train SRE models using pairs of stream images ranked in order of discharge by an annotator, obviating the need for discharge training data and thus facilitating monitoring streamflow conditions at streams without gauges. We also demonstrate a technique for converting SRE model predictions to stream discharge estimates given an estimated streamflow distribution. Using data and images from six small US streams, we compare the performance of SRE with conventional regression models trained to predict absolute discharge. Our results show that SRE performs nearly as well as regression models on relative flow prediction. Further, we observe that the accuracy of absolute discharge estimates obtained by mapping SRE model predictions through a discharge distribution largely depends on how well the assumed discharge distribution matches the field observed data.