In my opinion, it is acceptable to fly the flag at half staff for the death Whitney Houston.
And that is because The Head of the State of New Jersey deemed it to be appropriate.
Now, if that upsets some of the residents in that state, they can let the governor know when he comes up for re-election.
Furthermore, there are no laws on the books concerning who is and who is not eligible to have the flag flown at half mass in the event of their demise. The only things in place are traditions, precedents, and the usual policies and practices.
And, by the way. I served two tours of duty in Vietnam as an infantry soldier.