Most controllers for lower-limb robotic prostheses require individually tuned parameter sets for every combination of speed and incline that the device is designed for. Because ambulation occurs over a continuum of speeds and inclines, this design paradigm requires tuning of a potentially prohibitively large number of parameters. This limitation motivates an alternative control framework that enables walking over a range of speeds and inclines while requiring only a limited number of tunable parameters. In this work, we present the implementation of a continuously varying kinematic controller on a custom powered knee-ankle prosthesis. The controller uses a phase variable derived from the residual thigh angle, along with real-time estimates of ground inclination and walking speed, to compute the appropriate knee and ankle joint angles from a continuous model of able-bodied kinematic data. We modify an existing phase variable architecture to allow for changes in speeds and inclines, quantify the closed-loop accuracy of the speed and incline estimation algorithms for various references, and experimentally validate the controller by observing that it replicates kinematic trends seen in able-bodied gait as speed and incline vary.