Hi meteor, good luck in the search! Astronomers cause everyone much confusion by using "flat" in two separate ways.
The spacetime of cosmology has a distinguished space----that of an observer at rest relative to the expansion----relative to the CMB.
This SPACE can be flat without spacetime being flat.
Current observations of the CMB provide evidence of SPATIAL flatness. Spatial flatness has come to be generally accepted. There is a consensus that on the large scale space is flat or very very close to flat. Of course there is local curvature around stars and black holes etc.
Inflation scenario also predicts this spatial flatness, so the observation of spatial flatness is a lucky thing for the inflation scenario.
Observations indicate however that spacetime is not flat---because it expands---and therefore spacetime cannot have global Minkowski coordinates (that would be "flat-flat" really flat-out flat [:)])