  A stellar flare can brighten a planet in orbit around its host star,
producing a light curve with a faint echo. This echo, and others from
subsequent flares, can lead to the planet's discovery, revealing its orbital
configuration and physical characteristics. A challenge is that an echo is
faint relative to the flare and measurement noise. Here, we use a method, based
on autocorrelation function estimation, to extract faint planetary echoes from
stellar flare light curves. A key component of our approach is that we
compensate for planetary motion, measures of echo strength are then co-added
into a strong signal. Using simple flare models in simulations, we explore the
feasibility of this method with current technology for detecting planets around
nearby M dwarfs. We also illustrate how our method can tightly constrain a
planet's orbital elements and the mass of its host star. This technique is most
sensitive to giant planets within 0.1 au of active flare stars and offers new
opportunities for planet discovery in orientations and configurations that are
inaccessible with other planet search methods.
