Calculating gain of simple op-amp using KCL
The trick you missed (I think) is that, since this opamp is in a negative feedback loop, you can assume that the voltage between  the + and - inputs of the opamp is zero.

You can theoretically explain this by assuming that the opamp has an infinite gain so Vout = (Vin+ - Vin-) * infinite. This results in that the output voltage can have any value for input voltage = zero.

With that assumption (voltage at Vin- = zero, because Vin+ is grounded) and realizing that no current flows into or out of the opamp's inputs it is now much easier to calculate the currents and then the transfer function.