I wonder if this helps but ...Can't you just flip the parent Node2D.Transform2D directly? (There are even FLIP_X, FLIP_Y constants you may use)
https://docs.godotengine.org/en/stable/classes/class_transform2d.html
If you need another approach independent of using nodes and what Godot offers you, why not take all points from all collision shapes in the enemy, get most extreme values (highest and lowest coordinates) to obtain an overall center point for all shapes, and flip around it?. (Or even getting the sprite center point if that's your reference object).
Hope this helps you find a solution.
Cheers!