We present a new method for reconstructing a 3D flow field from multiple 3D Pulsed Wave Doppler echo images. A weakness of Doppler imaging is that only a 1D projection of the true 3D velocity (parallel to the echo beam direction) is measured. We propose a method which uses registered multiple Doppler views to calculate 3D flow vectors using a Least Mean Squares (LMS) minimisation process. Flow is expressed in a B-Spline basis, which allows scalability, regularisation and incorporation of derivative-based physical constraints. We investigate the reconstruction accuracy with respect to the amount of regularisation. We report experiments on phantom data and real cardiac data from a healthy volunteer, where we reconstructed flow through mitral and aortic valves. Results show that 3D flow can be reconstructed with an accuracy of approximately 20% of the 95th percentile of the velocity projection with our method.