If a MOSFET has infinite inner resistance (ro), how does current flow through it?
An ideal current source will have an infinite output impedance. You could connect a resistor in parallel with the current source but that resistor would need to have an infinite value R = infinite ohms because if the resistor value was any lower than infinite, current would flow through it and the current source (including resistor) would not be ideal anymore. The current would then depend on the voltage across the current source.

To model a non ideal current source the simplest way is to give that parallel resistor a finite value. That is what is done for a MOSFET in saturation mode as it is a non-ideal current source.

How the current flows can simply be determined by network equations. If you know the Vds of a MOSFET you can determine how much current flows through Ro.