What value determines the current flowing between two interconnected ICs?
The current is limited by the output impedance of the driver, and the input impedance of the receiver. A GPIO pin generally has very low output impedance in output mode (at most tens of ohms, likely less) and very high input impedance in input mode (millions of ohms), as long as the voltages remain between the voltage rails.

You shouldn't use an LED to reduce the voltage for level shifting because, aside from being a nasty hack, the LED's forward voltage depends on the current passing through it. Use a resistor divider instead.