We explore the dynamical structure of the protoplanetary disks surrounding HD 163296 and MWC 480 as part of the Molecules with ALMA at Planet Forming Scales (MAPS) large program. Using the $J = 2-1$ transitions of $^{12}$CO, $^{13}$CO and C$^{18}$O imaged at spatial resolutions of $sim 0.^{prime prime}15$ and with a channel spacing of $200$ ${rm m,s^{-1}}$, we find perturbations from Keplerian rotation in the projected velocity fields of both disks ($lesssim!5%$ of the local Keplerian velocity), suggestive of large-scale (10s of au in size), coherent flows. By accounting for the azimuthal dependence on the projection of the velocity field, the velocity fields were decomposed into azimuthally averaged orthogonal components, $v_{phi}$, $v_r$ and $v_z$. Using the optically thick $^{12}$CO emission as a probe of the gas temperature, local variations of $approx! 3$ K ($approx! 5 %$ relative changes) were observed and found to be associated with the kinematic substructures. The MWC 480 disk hosts a suite of tightly wound spiral arms. The spirals arms, in conjunction with the highly localized perturbations in the gas velocity structure (kinematic planetary signatures), indicate a giant planet, $sim! 1$ $M_{rm Jup}$, at a radius of $approx 245$ au. In the disk of HD 163296, the kinematic substructures were consistent with previous studies of Pinte et al. (2018a) and Teague et al. (2018a) advocating for multiple $sim! 1$ $M_{rm Jup}$ planets embedded in the disk. These results demonstrate that molecular line observations that characterize the dynamical structure of disks can be used to search for the signatures of embedded planets. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.
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