A moral nihilist can be an anarchist if his anarchism is not based on moral principles.
My anarchism is not based on some idealized set of voluntary interactions or the wet dream of a horizontal chain of confederations. Most of the time, it is a daily, practical, individual endeavor. It is the destructive intellect and physical might I project against any and all forms of oppression.
The sort of oppression I attack is most often the kind which affects only me or my tribe (my family and friends). I don't waste my time agitating for larger reforms in order to save humanity because it's 'the right thing to do.' Most of them are too stupid to see the bars in front of their faces anyway and like Casca, I detest the stink of mental proles (even though I hang out with a lot of them). Besides, this techno-globo-corporate-liberal society is a rolling stone that can't be stopped and we'll be dead before it morphs into anything else. So I enjoy the sun with my compatriots and topple whatever's in my way--whatever I am able to push off its pedestal.
This kind of anarchism should properly be called anarchy: not a program or a prescription, not even a philosophy, but a process. It is the blinding white heat that brings the sword of practical logic to a silvery boil and the tensed fist that buries it in the flesh of any and every god.
And it's about more than freedom and happiness. It's about being my own. I want my thoughts and my feelings and my actions to be mine to create and control. This is naked egoism. It's the practical creation at every moment of my individual will to power. Happiness and freedom are byproducts.
I suggest you read Max Stirner. In "The Ego and Its Own" he writes: "Freedom lives only in the realm of dreams! Owness, on the contrary is my whole being and existence, it is I myself. I am free from what I am rid of, owner of what I have in my power or what I control." He goes on to say that a man may lose his freedom, but "My own I am at all times and under all circumstances..."
Moralists want a god to sacrifice their lives to. Capitalist Anarchists deify natural rights and economic freedom behind horn-rimmed glasses. Social Anarchists with their beads and tye-dye worship society. The collective is their messiah and communism their heaven. And if you act against their god they seek to destroy you. You are their devil. And why? Because you refuse to be sacrificed. Because you want things to sacrifice themselves to you.
Morality is a mask for the weak to hide their inherent egoism from their own eyes. I suggest we clever ones pull it off and laugh like Momus.