Your variable is defined in your player script that extends a KinematicBody2D, right?
I think you should access it by simply using dot notation.
onready var player = $Player_node
var facing_x = player.facing_x #copy value from node
facing_x = -1 #change variable in function
player.facing_x = -1 #change value in node
If you change
facing_x by assigning a new value, it happens only locally (within the
_ready function but does not apply to the actual Player node).
Anyway if you only need to change the sprite you could simply use