  We present precise measurements of radial (RV) and projected rotational
($v\sin{i}$) velocities, effective temperatures, and surface gravities of a
sample of 258 M6 to L2 dwarfs with multi-epoch, high-resolution
($\lambda/\Delta\lambda$ = 22500), near-infrared (1.514-1.696 $\mu$m)
spectroscopic observations reported in the Apache Point Observatory Galactic
Evolution Experiment (APOGEE) Data Release 17. The spectra were modeled using a
Markov Chain Monte Carlo forward-modeling method which achieved median
precisions of $\sigma_\text{RV}$ = 0.4 km s$^{-1}$ and $\sigma_{v\sin{i}}$ =
1.1 km s$^{-1}$. One-half of our sample (138 sources) are previously known
members of nearby young clusters and moving groups, and we identified three new
kinematic members of the Argus or Carina Near moving groups, 2MASS
J05402570+2448090, 2MASS J14093200+4138080, and 2MASS J21272531+5553150.
Excluding these sources, we find that the majority of our sample has kinematics
consistent with the Galactic thin disk, and eleven sources are associated with
the intermediate thin/thick disk. The field sample has a velocity dispersion of
38.2$\pm$0.3 km s$^{-1}$, equivalent to an age of 3.30$\pm$0.19 Gyr based on
empirical age-velocity dispersion relations; and a median $v\sin{i}$ of 17 km
s$^{-1}$. For 172 sources with multi-epoch observations, we identified 37 as
having significant radial velocity variations, and determined preliminary orbit
parameters for 26 sources with four or more epochs. For 40 sources with
photometric variability periods from the literature less than 5 days and
$v\sin{i}$ $>$ 20 km s$^{-1}$, we find a decline in projected radii $R\sin{i}$
with age congruent with evolutionary models. Finally, we also present
multi-epoch RV and vsini measurements for additional 444 candidate ultracool
dwarfs.
