I forgot to add butter to my king cake dough

Unfortunately, if you attempt to combine the butter into the already risen dough, the dough's structure would most likely get ruined.

I wouldn't stress too much over the forgotten butter in the dough though, as the filling will consist of butter as well. Also, you may be able to salvage some flakyness by gently folding in thin sheets of butter into the dough.

That’s a shame after you did all that work. (oops)
I’d make a little melted butter and vanilla and brush the cake w/that (lightly) before you frost it.