There's a helpful question here on the notion of "freedom toward death" (Can "freedom toward death" have 'freedom' translated out of it?).
For this question, I find the first sentence to be a bit imprecise:
My "freedom toward death" (Sein und Zeit, p266) is key for authenticity, according to Heidegger.
Authenticity for Heidegger is precisely to be conscious of one's being towards death. So my freedom towards death is the ability to relate to the possibility of one's own death freely and without looking away from it.
Does any of the secondary literature claim that it is for others, not for me? Either correcting Heidegger, or his interpreters?
it does not make sense to speak of "it" (this freedom?) as being for others rather than for the Da-Sein (the I) because the freedom is precisely to face up to one's own utmost possibility in death.
I'm asking because I've read it claimed that authenticity is freedom to be whatever you want (a fascist, a communist, whatever).
This definition of freedom as radical freedom is more Sartre than Heidegger. For Sartre, authenticity is to be the source of one's own values and to not merely receive anything passively. In other words, it is to recognize that all choices and all of the contexts for choices stem from a radically free self. (This is Sartre's view -- I am not claiming it is true here).
In contast, Heidegger's idea of authenticity (more properly Eigentlichkeit) is being one's own self -- which for Heidegger is a being that will eventually die. Thus, the "authentic" element here is not that I believe I make all of the choices about my life and values but rather that I recognize that my existence is predicated on the possibility and eventual actuality of my own death. The only sense in which others can have my "freedom towards death" is that they can kill me and that is one possible way that I can die.
It should be noted that a common accusation against Heidegger is that he lacks a political philosophy and an ethics. In fact, authenticity (again Eigentlichkeit) is according to Heidegger not a moral category. (This does not mean Heidegger is right about its nature).