I don't get a headache when drinking the SWF, but I have woken up with headaches on occasion during a cleanse that I attribute to detox symptoms.
FYI, "hypertension" is just a single word that means "high blood pressure." They are one and the same.
Yes, it is perfectly safe for someone who has high blood pressure to drink the SWF. Two teaspoons of non iodized sea salt in one quart of warm water provides the same concentration of salt that is in our blood. For that reason, the salt and the water do not tend to get absorbed into our gastrointestinal tract. That is why it is called a "flush." Adding that concentration of salt allows the water to not get absorbed so it will "flush" all the way through the small and large intestines, carrying the bile (that contains the toxins the liver has processed and excreted) out of the body with it. (And of course, the two teaspoons of salt also leave the body at that time.)
Keep in mind that if someone drinks the SWF and they do not experience the expected elimination, Burroughs suggests that you try adding a bit more salt until it does work for you. That is because The Creator does not stamp us all out from the same cookie cutter. We are each individual miracles.
Another thing to keep in mind, for those folks who just cannot get the SWF to work for them, or for those folks who do have high blood pressure and simply are too afraid to trust that the SWF is safe for them, Burroughs says it is okay to not drink the SWF, but to instead drink the senna tea twice a day, just before going to bed and again on awakening in the morning.