I guess a flexitarian could be a nutritarian, but not necessarily so.
As a nutritatian, I am edging towards eating meat or fish, but if I do that I want it to be wild and not farm bread, and I would prefer to kill or catch it myself. At least then I get some feedback on what I am doing to the environment, for example finding out that the rainbow trout I ate two weeks ago was full of eggs when I gutted it.
I have come a long way from the times when what I ate was mostly junk and processed food, 18 months ago.