Many diseases of the eye are associated with alterations in the retinal vasculature that are possibly preceded by undetected changes in blood flow. In this work, a robust blood flow quantification framework is presented based on optical coherence tomography (OCT) angiography imaging and deep learning. The analysis used a forward signal model to simulate OCT blood flow data for training of a neural network (NN). The NN was combined with pre- and post-processing steps to create an analysis framework for measuring flow rates from individual blood vessels. The framework's accuracy was validated using both blood flow phantoms and human subject imaging, and across flow speed, vessel angle, hematocrit levels, and signal-to-noise ratio. The reported flow rate of the calibrated NN framework was measured to be largely independent of vessel angle, hematocrit levels, and measurement signal-to-noise ratio. In vivo retinal flow rate measurements were self-consistent across vascular branch points, and approximately followed a predicted power-law dependence on the vessel diameter. The presented OCT-based NN flow rate estimation framework addresses the need for a robust, deployable, and label-free quantitative retinal blood flow mapping technique.