Migraines and hot flashes are not necessarily menopause symptoms but rather can be from hormonal imbalance issues. It sounds like your doctor is trying to regulate the hormones your ovaries are producing with the low dose birth control pills to try to eliminate the migraines and hot flashes. My doctor had recommended low dose birth control pills for me when I was having issues following my hysterectomy.
Have you ever spoken with a neurologist regarding your migraines? There may be some options for treating them besides birth control pills if you would prefer to try that route. My neurologist preferred I not use any hormone, fearing it would worsen my migraines. So instead, I started a prophylactic migraine med which I took every single day. That didn't take care of the hot flashes but they lessened over time. Your doctor may be able to off options specifically for the hot flashes if you choose not to take the birth control pills.
If you have concerns, sit down and discuss all of them with your GYN. You can also talk to your primary care physician about your options. Your GP may agree with your GYN or may have some other options you could consider.
In the meantime, it would help if you could keep a journal of your symptoms. This might let you see if there are triggers other than your hormones causing the migraines and hot flashes. For instance, while I tend to get more hot flashes at certain times of the month, I also can have them when my sugar is way off, if I have spicy food, or am stressed. The same can be true for migraines--lack of sleep, stress, and for some certain foods.
Also, by any chance did you have endometriosis? That may be another reason your doctor is prescribing the birth control pills. With endo, any estrogen needs to be balanced with progesterone or progestin. So, if you need estrogen to eliminate migraines and/or hot flashes, you also need the progestin in the bcp to help keep any endo at bay!