I am 51 have had a hysterectomy have one ovary and am having severe hot flushes.how long will this last?

Good chance is that ovary has atrophied and is no longer functioning. Go to your Dr and see about hormone replacement therapy. I gradually phased out my hormone pills when I reached 60. My ovaries had ceased to function due to a tubal ligation that interfered with the supply to my ovaries. When i had a hysterectomy at age 40 my ovaries had not been functioning for about 8 years.