  The hot, X-ray-emitting phase of the circumgalactic medium of massive
galaxies is believed to be the reservoir of baryons from which gas flows onto
the central galaxy and into which feedback from AGN and stars inject mass,
momentum, energy, and metals. These effects shape the velocity fields of the
hot gas, which can be observed via the Doppler shifting and broadening of
emission lines by X-ray IFUs. In this work, we analyze the gas kinematics of
the hot circumgalactic medium of Milky Way-mass disk galaxies from the TNG50
simulation with synthetic observations to determine how future instruments can
probe this velocity structure. We find that the hot phase is often
characterized by outflows from the disk driven by feedback processes, radial
inflows near the galactic plane, and rotation, though in some systems the
velocity field is more disorganized and turbulent. With a spectral resolution
of $\sim$1 eV, fast and hot outflows ($\sim$200-500 km s$^{-1}$) can be
measured, depending on the orientation of the galaxy on the sky. The rotation
velocity of the hot phase ($\sim$100-200 km s$^{-1}$) can be measured using
line shifts in edge-on galaxies, and is slower than that of colder gas phases
but similar to stellar rotation velocities. By contrast, the slow inflows
($\sim$50-100 km s$^{-1}$) are difficult to measure in projection with these
other components, but may be detected in multi-component spectral fits. We find
that the velocity measured is sensitive to which emission lines are used.
Measuring these flows will constrain theories of how the gas in these galaxies
evolves.
