How does current flow in this circuit
The current \$I_X\$ (flowing from \$V_X\$) is made from two parts: -

\$g_m\cdot V_{GS}\$ and
the current flowing through \$R_0\$

The current flowing through \$R_0\$ = \$\dfrac{V_D - V_S}{R_0}\$
Also, you have shown the gate grounded in your circuit and that should not be the case.