  We investigate the effects of Dynes pair-breaking scattering rate $\Gamma$ on
the superfluid flow in a narrow thin-film superconductor and a semi-infinite
superconductor by self-consistently solving the coupled Maxwell and Usadel
equations for the BCS theory in the diffusive limit for all temperature $T$,
all $\Gamma$, and all superfluid momentum. We obtain the depairing current
density $j_d(\Gamma, T)$ and the current-dependent nonlinear kinetic inductance
$L_k(j_s, \Gamma, T)$ in a narrow thin-film and the superheating field
$H_{sh}(\Gamma, T)$ and the current distribution in a semi-infinite
superconductor, taking the nonlinear Meissner effect into account. The
analytical expressions for $j_d(\Gamma,T)|_{T=0}$, $L_k(j_s, \Gamma,
T)|_{T=0}$, and $H_{sh}(\Gamma, T)|_{T=0}$ are also derived. The theory
suggests $j_d$ and $H_{sh}$ can be ameliorated by reducing $\Gamma$, and $L_k$
can be tuned by a combination of the bias current and $\Gamma$. Tunneling
spectroscopy can test the theory and also give insight into how to engineer
$\Gamma$ via materials processing. Implications of the theory would be useful
to improve performances of various superconducting quantum devices.
