This means that and which give exponential inflation. We have . Thus the term is entirely negligible. This is an improtant distinction. This is perfectly OK with inflation which simply dilutes the curvature.
Inflation actually says nothing about the value of k .
It simply predicts that at the end of inflation. On Earth, the reason many people believe the Earth is flat is because we cannot see beyond the horizon. Up to the horizon it looks flat. If we could see beyond the horizon we would see the curvature. Similarly for our universe.