We present a 5.4-sigma detection of the pairwise kinematic Sunyaev-Zel'dovich (kSZ) effect using Atacama Cosmology Telescope (ACT) and Planck CMB observations in combination with Luminous Red Galaxy samples from the Sloan Digital Sky Survey (SDSS) DR15 catalog. ACT maps in the 90 and 150GHz bands are used (data release 5, DR5), which overlap with the SDSS DR15 over 3,700 sq. deg. Component separated maps from the ACT DR4 are also used, which overlap with SDSS DR15 over 2,089 sq. deg. A total of 343,647 galaxies were used to identify and locate galaxy groups from which the kSZ signal is extracted using aperture photometry and the pairwise kSZ estimator with bootstrapped covariances. Theoretical predictions of pairwise velocities are used to fit optical depth estimates for five luminosity-selected tracer samples. Optical depths presented here are compared with thermal SZ effect results for the same galaxy sample in a companion paper (Vavagiakis 2021).