I found it, we were considering Satan having had each King from a different mother... that way their special abilities would come from the mother and Satan would only have the flames.
So, I think either Satan:
- aside from getting rid of whatever other demons of his same kin that existed, devoured the power of the most powerful demons of the other kings to rule them and then passed down an specific power of those to each of the kings.
- he had a son with a demoness of each kin so each king has the power of their mother amplified by Satan's strength, also this served him to have a blood bond to each kin.
- he simply had his sons devour the power of a different kin each, after they were born.