1) You have the 5V power supply connected to the input of the opamp instead of powering it.
2) You have the output of the opamp connected to the phone but its output cannot supply enough current to power the charging circuit.
3) You have the LED in series with the very high resistance input of the opamp so it will never light.
I used a 3.3 ohm resistor as a current sensor for the charging current to the phone.
I used the first opamp as an amplifier with a gain of 101 times. Then when the charging current is more than 10mA the output of this opamp is high which turns off the LED. When the charging current is less than 10mA then the output of the opamp goes low which lights the LED.
I disabled the second opamp.
An LM358 dual opamp is used because it is available almost eveywhere and has inputs that work at a voltage as low as ground.