Whether anyone should take flax in any form when hypothyroid may be a matter of trial and error.
I had a severe reaction to ground flaxseed just before I began thyroid treatment. I was hypothyroid when I started eating it, but undiagnosed. It appeared to completely shut down whatever natural thyroid function I had aat that time, judging by the symptoms it caused.
Now that I'm in treatment, and doing pretty well, my doctor wants me to take flax oil capsules for their omega-3 benefit. He's an alternative practitioner, and he says he's never heard of a reaction to flax like I had, although he doesn't doubt that it happened. He often has thyroid patients take it without problems. Naturally, I'm pretty reluctant to risk that the oil might have the same effect as the seed; I don't want to enter Myxedema Land again.... Boy, that was rough! So to appease him, I've been taking fish oil caps instead.
So, I can't tell you for sure if flax oil is bad for you. Maybe the oil is fine, and the seed isn't .... Maybe either one is ok if you're in treatment, but will shut down your gland if you aren't in treatment .... Maybe I had some kind of allergic reaction to it that you wouldn't have .... ???? Lots of 'maybes'.
I'd say... if your thyroid levels are good, and the symptoms of hypoT have abated, it's probably ok to take the oil for your meno symptoms. Just don't ask me to take any!