We used the Keck Planet Imager and Characterizer to obtain high-resolution (R similar to 35,000) K-band spectra of kappa Andromedae b, a planetary-mass companion orbiting the B9V star, kappa Andromedae A. We characterized its spin, radial velocity, and bulk atmospheric parameters through use of a forward-modeling framework to jointly fit planetary spectra and residual starlight speckles, obtaining likelihood-based posterior probabilities. We also detected H2O and CO in its atmosphere via cross correlation. We measured a vsin(i) value for kappa Andromedae b of 38.42 +/- 0.05 km s(-1), allowing us to extend our understanding of the population of close-in bound companions at higher rotation rates. This rotation rate is one of the highest spins relative to breakup velocity measured to date, at close to 50% of breakup velocity. We identify a radial velocity -17.35-0.09+0.05 km s(-1), which we use with existing astrometry and radial velocity measurements to update the orbital fit. We also measure an effective temperature of 1700 +/- 100 K and a log(g) of 4.7 +/- 0.5 cgs dex.