In my dictionary, there exists only "add insult to the injury." It means to make a relationship with another person even worse by offending him as well as actually harming him.
To improve my writing, here I venture my premature example:
After giving his woman a good lash, Jack added insult to her injury by letting her feel the lash of his tongue in public.
As for to add injury to the insult, I think we need some help from other members of experts. Personally, I presume it could work and make sense except that it assumes a somewhat different meaning from to add insult to injury.




