Clearing the buffer is generally not a good idea. The old flush() method did that by throwing away random amounts of unread data. I can't see how that is a good idea, unless you are resting code that re-syncs with a sender.
If that is not the goal, then every character sent was sent with the expectation that it would be important, and, therefore, read.
Why would you not want to read that data, if you sent it?
If you don't want the Arduino to have to read the data, don't send it.