A high-intensity laser pulse propagating through a medium triggers an ionization front that can accelerate and frequency upshift the photons of a second pulse. The maximum upshift is ultimately limited by the accelerated photons outpacing the ionization front or the ionizing pulse refracting from the plasma. Here, we apply the flying focus-a moving focal point resulting from a chirped laser pulse focused by a chromatic lens-to overcome these limitations. Theory and simulations demonstrate that the ionization front produced by a flying focus can frequency upshift an ultrashort optical pulse to the extreme ultraviolet over a centimeter of propagation. An analytic model of the upshift predicts that this scheme could be scaled to a novel tabletop source of spatially coherent x rays.