Bendiness = space-time curvature.
And yes, it is flat (k=0) for the EdS model. Essentially it is the epoch at which only matter is thought to dominate (no contributions from radiative pressure or dark energy, $Lambda$).
It is only a model. The EdS universe is thought of as a static Universe which is expanding indefinitely. It just makes solving certain equations in Cosmology a little easier, but it was perhaps due to Einstein's stubbornness in accepting a dynamic Universe.
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