Read ESP8266 serial console with Arduino UNO

Your Adruino code looks complicated, and I'm not sure if it's correct, or if you're overwriting the variable IncomingString in the while loop.

The sample code for serial input from https://www.javatpoint.com/arduino-serial-available:

void loop( ) // loop function that executes repeatedly  
{  
if(Serial.available( ) > 0) //  It will only send data when the received data is greater than 0.  
{  
arrivingdatabyte = Serial.read( );  // It will read the incoming or arriving data byte  
Serial.print("data byte received:");  
Serial.println(arrivingdatabyte, DEC); // here, DEC means Decimal  
}  
}  

I'd suggest to remove the while and the true/false in your code, and change it according to the sample code.