The Kingsguard does not flee.

The Kingsguard, also known poetically as the White Swords or white cloaks, are the royal bodyguards of the Iron Throne. Supposedly the finest knights in the Seven Kingdoms, they are sworn to protect their king and the royal family with their own lives, to obey his commands, and to keep his secrets. They are sworn for life and are forbidden from owning land, taking a wife, or fathering children, although they can have non-hereditary commands, such as being warden or Hand of the King.