First. The universe is flat and not negativity curved because whatever dark energy is made from represented by the cosmological constant adds to the side of the density in the first Friedman equation:
$$\left(\frac{\dot{a}}{a}\right)^2 - \frac{8πGρ}{3} -\frac{Λc{^2}}{3} = -\frac{kc{^2}}{a^2}$$
So that the curvature $k$ is zero.
Second. The universe is not flat. It just looks flat because inflation, caused by the cosmological constant, blew up small flat patches of space.
These two explanations of why the universe is flat, have the same root (cosmological constant) but to me at least seem to contradict with each other. If they are indeed the same explanation done differently please explain.
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