  Estimating stellar ages is important for advancing our understanding of
stellar and exoplanet evolution and investigating the history of the Milky Way.
However, ages for low-mass stars are hard to infer as they evolve slowly on the
main sequence. In addition, empirical dating methods are difficult to calibrate
for low-mass stars as they are faint. In this work, we calculate ages for
Kepler F, G, and crucially K and M dwarfs, using their rotation and kinematic
properties. We apply the simple assumption that the velocity dispersion of
stars increases over time and adopt an age--velocity--dispersion relation (AVR)
to estimate average stellar ages for groupings of coeval stars. We calculate
the vertical velocity dispersion of stars in bins of absolute magnitude,
temperature, rotation period, and Rossby number and then convert velocity
dispersion to kinematic age via an AVR. Using this method, we estimate
gyro-kinematic ages for 29,949 Kepler stars with measured rotation periods. We
are able to estimate ages for clusters and asteroseismic stars with an RMS of
1.22 Gyr and 0.26 Gyr respectively. With our Astraea machine learning
algorithm, which predicts rotation periods, we suggest a new selection
criterion (a weight of 0.15) to increase the size of the McQuillian et al.
(2014) catalog of Kepler rotation periods by up to 25%. Using predicted
rotation periods, we estimated gyro-kinematic ages for stars without measured
rotation periods and found promising results by comparing 12 detailed
age--element abundance trends with literature values.
