When attempting to interpret or control unsteady flows, we often want access to the full velocity field (i.e., state). This is possible with simulations or experimental techniques like tomographic particle image velocimetry (PIV). Unfortunately, PIV is often not an option, and alternative techniques tend to provide partial measurements (e.g., streaklines, schlieren imaging, and surface pressure measurements). When only partial measurements are available, determining the velocity field appears intractable. However, the Navier-Stokes equations are dissipative, which leads to the expectation that trajectories attract towards a low-dimensional manifold of dimension N. When this is true, Whitney's (strong) embedding theorem implies that there exists some function that maps almost any 2N measurements to the full velocity field. Although this mapping ought to exist, we do not know how to find it. Fortunately, approximating functions from data is now common with machine learning (e.g., autoencoders and superresolution). Here, we present a method for reconstructing velocity fields directly from streakline measurements. The success of this work will offer a rapid method for experimentalists to determine velocity fields from simple, accessible measurements. Specifically, we generate simulated data to train neural networks (NN) to map streaklines to velocity fields, which can be used in experiments. First, we validate this approach on simulations of 2D Kolmogorov Flow and 3D Couette flow. Our approach achieves highly accurate flow reconstruction using streakline measurements as an input to a convolutional NN. We will also present preliminary results on using these NNs trained on simulated data to predict turbulent experimental channel flow. By injecting two streaklines in the experiment, we use one to predict the flowfields and the other to validate the accuracy of our predictions.