Opioids are given routinely for severe migraine and once the migraine is a bad one, opioids are the only thing that works. More than your average toothache dose too.
That said, we do not know how serious this problem is. If it is as serious as described (plausible), her health is not up to the task.
My sister would get these migraine/cluster headaches about 3-4 times a year. She would be down and in the dark...taking 10-15mg of oxycodone every three hours...for at least one full day, sometimes up to 2 days.
She is a nurse.
She told me she was lucky as she had met people who get it that bad 2-3 times per month.
It's a legitimate health concern for the CinC. She would not be fit to command a warship at sea if as chronic as described. Nor would she qualify as a Brigadier in the Army...probably not Battalion CO.
It has nothing to do with her capabilities when well.
What about Tylenol 3 with Codene (narcotic)?