No. Profits made from royalties go primarily into funding The King Center. http://www.thekingcenter.org/

And who works for the King Center? MLK's kids.

So yes, royalties go to the King Center, which at least in part, go to his children, including MLK III.

https://en.wikipedia.org/wiki/Martin_Luther_King_III

And this is bad...how? They are working to further MLK's goals.

I haven't seen anything that they've done of recent merit in the news lately.