Serial communication between two Arduino Nano’s

is there a way to clear the serial buffer after round one?

Just do

while(Serial.available) // while there are bytes in the serial buffer
{
Serial.read();  //read the bytes and throw them away
}

That will empty the serial buffer.

I am curious why you need 2 Nanos. If you are short on pins, note that the analog inputs can be used as digital pins (6 pins).

And why all the code in setup with a while(1). That is what loop() is for.