BirdOne To match the hand holding the item even if the skeleton is flipped, I think the general approach is to use method 2 of Spinebot's answer, which is to use skins for the asymmetric parts. Or, if the item images were not originally included in the skeleton and would be added at runtime, then the skeleton would only have empty slots for adding item images, and the visiblity would be switched to which slots they are in according to the direction the character is facing.
As for the kicking animation, I think the only way to match this would be to have a kicking animation for each leg and switch the animation that plays according to the direction the character is facing.