Emptying (Flushing) Serial1 INPUT Buffer

while (Serial1.available()) Serial1.read();

while (Serial1.read() > 0) {}

Warning: If characters are still arriving this will not guarantee that the buffer will be empty next time you look. To get closer to that:

while (Serial1.available()) {Serial1.read(); delay(10);}

while (Serial1.read() > 0) {delay(10);}