Hydrodynamic-like electron flows are typically modeled using the Stokes-Ohm equation or a kinetic description that is based on a dual-relaxation-time approximation. Such models assume a short intrinsic mean free path ${\ell }_e$ due to momentum-conserving electronic scattering and a large extrinsic mean free path ${\ell }_{\mathrm{\text{MR}}}$ due to momentum-relaxing impurity scattering. This assumption, however, is overly simplistic and falls short at low temperatures, where it is known from exact diagonalization studies of the electronic collision integrals that another large electronic mean free path ${\ell }_o$ emerges that describes long-lived odd electron modes—this is sometimes known as the tomographic effect. Here, using a matched asymptotic expansion of the underlying Fermi-liquid kinetic equation with multiple electron relaxation times, we derive an asymptotic theory for tomographic flows in arbitrary smooth boundary geometries. Our key results are a set of governing equations for the electron density and electron current, their slip boundary conditions (which are applied at diffuse boundaries), and boundary layer corrections near diffuse edges. We find that the tomographic effect strongly modifies previous hydrodynamic theories for electron flows: In particular, we find that (i) an equilibrium is established in the bulk, where the flow is governed by Stokes-Ohm-like equations with significant finite-wavelength corrections, (ii) the velocity slip condition at the boundary is strongly modified and not accounted for by the widely used hydrodynamic slip-length condition, (iii) a large kinetic boundary layer of width arises near diffuse boundaries, which is much larger than in conventional near-hydrodynamic theories, and (iv) all these effects are strongly suppressed by an external magnetic field. We illustrate our findings for electron flow in a channel. The equations derived here provide a comprehensive framework for future studies of tomographic flows in smooth geometries.