  We explore the possible values of the $\mu \to e \gamma$ branching ratio,
$\text{BR}(\mu\rightarrow e\gamma)$, and the electron dipole moment (eEDM),
$d_e$, in no-scale SU(5) super-GUT models with the boundary conditions that
soft supersymmetry-breaking matter scalar masses vanish at some high input
scale, $M_{\rm in}$, above the GUT scale, $M_{\rm GUT}$. We take into account
the constraints from the cosmological cold dark matter density, $\Omega_{CDM}
h^2$, the Higgs mass, $M_h$, and the experimental lower limit on the lifetime
for $p \to K^+ \bar \nu$, the dominant proton decay mode in these super-GUT
models. Reconciling this limit with $\Omega_{CDM} h^2$ and $M_h$ requires the
Higgs field responsible for the charge-2/3 quark masses to be twisted, and
possibly also that responsible for the charge-1/3 and charged-lepton masses,
with model-dependent soft supersymmetry-breaking masses. We consider six
possible models for the super-GUT initial conditions, and two possible choices
for quark flavor mixing, contrasting their predictions for proton decay with
versions of the models in which mixing effects are neglected. We find that
$\tau\left(p\rightarrow K^+ \bar{\nu}\right)$ may be accessible to the upcoming
Hyper-Kamiokande experiment, whereas all the models predict
$\text{BR}(\mu\rightarrow e\gamma)$ and $d_e$ below the current and prospective
future experimental sensitivities or both flavor choices, when the dark matter
density, Higgs mass and current proton decay constraints are taken into
account. However, there are limited regions with one of the flavor choices in
two of the models where $\mu \to e$ conversion on a heavy nucleus may be
observable in the future. Our results indicate that there is no supersymmetric
flavor problem in the class of no-scale models we consider.
