There are more than one way to view the description of the universe as flat. There is the description of an open, flat or closed universe in terms of it's fate, expansion forever away from gravity, or ...
My understanding is that dark energy, or equivalently a positive cosmological constant, is accelerating the expansion of the universe and I have read that this gives empty space-time positive ...
There is not-so-rough evidence that at very large scale the universe is flat. However we see everywhere that there are local lumps of matter with positive curvature. So i have several questions ...