Bio-inspired sensing modalities enhance the ability of autonomous vehicles to characterize and respond to their environment. This paper concerns the lateral line of cartilaginous and bony fish, which is sensitive to fluid motion and allows fish to sense oncoming flow and the presence of walls or obstacles. The lateral line consists of two types of sensing modalities: canal neuromasts measure approximate pressure gradients, whereas superficial neuromasts measure local flow velocities. By employing an artificial lateral line, the performance of underwater sensing and navigation strategies is improved in dark, cluttered, or murky environments where traditional sensing modalities may be hindered. This paper presents estimation and control strategies enabling an airfoil-shaped unmanned underwater vehicle to assimilate measurements from a bio-inspired, multi-modal artificial lateral line and estimate flow properties for feedback control. We utilize potential flow theory to model the fluid flow past a foil in a uniform flow and in the presence of an upstream obstacle. We derive theoretically justified nonlinear estimation strategies to estimate the free stream flowspeed, angle of attack, and the relative position of an upstream obstacle. The feedback control strategy uses the estimated flow properties to execute bio-inspired behaviors including rheotaxis (the tendency of fish to orient upstream) and station-holding (the tendency of fish to position behind an upstream obstacle). A robotic prototype outfitted with a multi-modal artificial lateral line composed of ionic polymer metal composite and embedded pressure sensors experimentally demonstrates the distributed flow sensing and closed-loop control strategies.