Every time I’ve killed king slime (along with the treasure bag) I have gotten a royal crown, 11 times! And there is a wiki dude.
Whoops, that's my bad. It always drops the crown first and only drops the gown if you have the crown in your inventory. If you put the crown away or sell it or anything it'll never drop the gown. Huge oversight on my part. I've got a collection of tweaks and bugfixes that I need to do, I'll have that out in a week or so.