Flow of current in a simple inverting amplifier circuit
But assuming an ideal op-amp (drawing no current) and an ideal voltmeter (drawing no current), where does the current flow to (in order to satisfy Kirchhoff's current law)?


The inputs of an ideal op-amp draw no current.

But the output behaves like an ideal voltage source --- it can source or sink as much current as needed to respond to signals at the inputs. For purposes of Kirchoff's current law you can imagine the other side of this voltage source being connected to ground inside the op-amp symbol.

Kirchoff's current law is satisfied by the output pin sinking current so that the R2 current equals the R1 current.