Just reading the passage you quoted, I have several initial thoughts. One is his complaint that post-Left anarchy (of the three listed tendencies, the only one I consider myself to be a part of is post-Left anarchy so that is the only one which I am going to discuss) is at odds with anarchism. Obviously this depends on the definition of anarchism; if the definition is simply a philosophy which states that anarchy is both desirable and possible, than obviously it is at odds with HIS anarchism not anarchism in general. He seems to be foolish enough to believe that there is some correct anarchist orthodoxy, if he denies this he should explain what about post-Left anarchy is at odds with anarchism in general and not just his, apparently only, interpretation of such (I dont see him being able to do so). But in any case, I agree with the saying that is apparently common in Greece "We fight for anarchy, not anarchism".
Next, is his utterly dishonest assertion that post-Left anarchy is anti-communist. Zerzan may qualify, but to imply post-Left anarchy in general does is to claim guilt by association and fail at the construction of an actual argument. If Andrew Flood had read post-Left anarchist ideas he would know that all post-Left anarchists are anti-capitalist and writings from the tendency include things like "We embrace what is best in individualism; we embrace what is best in communism", "Individualism and Communism: Aims of Anarchist Revolution". Flood would not be able to find any post-Left anarchist quotes which are pro capitalist. Period.
I don't know if there is a "formal response" to Flood's sad and pathetic lack of an argument, but I do know that producing texts like this thoroughly demonstrates Flood is doing a fantastic job discrediting himself.