Hi
A month or so ago,
@chrisicebox had created a great custom script to help me with flipping 2D characters using sprites unity complex for animation. (The script and its description can be found here)
I'd had this issue with it from the beginning, but decided to get to fixing it later. The issue is - The character doesn't flip on its center. Instead, it flips on its edge, meaning the character jumps a little distance everytime it flips. The picture attached below should make it clearer -

I've highlighted the axis upon which it turns in red.
Comments
What was the link? When flipping, does the position of either the sprite child or the root object change?
The yellow circle is the centre-point of the root object, as AC places it there automatically. The position of your Anima2D rig / spritemeshes is not fixed, but they do have to be placed correctly when first setting up the character and animations.
It may be that you have to re-make the Anima2D rig, but I don't know what your hierarchy looks like. You should have your Anima2D rig / SpritesMeshes parented to a shared GameObject that serves as the character's Sprite child (which should be located at 0,0,0). It may be that adding a second child object in between allows you to reposition the whole rig/spritesmeshes without affecting the root or sprite child.