Christoffel Symbols in Flat Space-Time Does it make sense to talk about Christoffel symbols in flat space time? Do they have non-zero values? I understand that the Christoffel symbols appear as an indication of curvature in space. So, are they non-existent in flat space-time?

Yes, it makes sense to talk about Christoffel symbols in flat spacetime. Every coordinate system has associated Christoffel symbols. On Minkowski spacetime in the standard coordinates, the Christoffel symbols are all zero. But in different coordinates (e.g., spherical coordinates), they will not be zero. The Christoffel symbols contain information about the intrinsic curvature of the spacetime _and_ about the "curvature of the coordinates".