When we say that the universe is flat, what does that really mean? The possible topologies of space-time are: open, flat and closed. A useful parameter when talking about the curvature of the universe is the density parameter given by omega (Ω) where Ω = Ωm + Ωrel + ΩΛ. The first term is the mass density given by ordinary, baryonic matter. The second term is the equivalent mass density of relativistic particles made up of electromagnetic energy and neutrinos. The last term is the effective mass of the universe dominated by dark energy (the cosmological constant.) The density parameter of the universe is given by the density divided by the critical density to result in a flat universe. If the density in the universe is exactly equal to the required density to inhabit a flat universe, Ω will be equal to 1. Current measurements give that Ω = 1.005 +/- 0.0007. Our universe is nearly flat! This can be seen using the Cosmic Microwave Background using a simple relationship.
Since the fluctuations in the CMB data are standard rulers, the curvature of the universe will determine the angular size of the fluctuations and thus the apparent size of the fluctuations will suggest the curvature of the universe. In an open universe, the curvature of space-time will distort light such that the fluctuations will seem smaller than they really are. On the contrary, in an open universe, the fluctuations will seem larger than they really are. In complete accordance with simulations of a flat universe, the fluctuations of the CMB data signify a flat universe: the universe has nearly exactly the critical density to result in a flat universe.