OK, let me make a clarification. Indeed, the phrase "author of sin" does really need clarification. This is one way of clarifying the idea, by pointing out that on a Calvinist view the difference between a world in which I sin and one in which I don't is the result of action by God, while on an Arminian view, it looks like a world in which I don't sin is not a world that God has the power to actualize. I mean here a world identical to this one up to t. God may know this by consulting his middle knowledge, he may know it by simple foreknowledge, or he may not find out about it until it happens (open theism).
On some libertarian views, my decision today affects God's decision to instantiate the world, even though that took place before the foundation of the world. George Mavrodes, for example, is a defender of backwards causation. But all these views make my choice the deciding factor in whether I sin or not.
I take it that when the Calvinistic God is called the author of sin, however, the intent is either to argue either that God is morally blameworthy for sin, or that humans are not blameworthy for sin. The second of these claims requires an incompatibilist account of blameworthiness and, in particular, fitness for retribution.
I think a lot of secular compatibilists, such as Dennett or Schlick, see retribution as a barbarous notion, and think that holding a person morally responsible is a matter of behavior modification. In fact, my master's thesis in philosophy at Arizona State developed that idea. A person could accept some forms of compatibilism while being a cheerful incompatibilist (or incoherentist--the idea of retribution makes no sense) about retribution. A Calvinist doesn't have those options open to him. He is committed to the idea that compatibilist freedom is sufficient to make a sinner fit for retribution.
The first of these claims is that God being the author of sin in the sense described makes him blameworthy for sin. Now the point made by then-atheist/compatibilist Flew would hold if compatibilism were true, namely, that God could have created the world in such a way that everyone freely does what is right. That Calvinist will have to argue that could have does not mean should have, and that God has a reason for creating a world with sinners and even reprobates as opposed to the world of Mr. Rogers, where everyone freely does what is right.
The Calvinist response is typically that God decrees sin so that the sacrifice of Christ can be possible, and God decrees reprobation because the existence of reprobates gives God the opportunity to glorify himself through his wrath against unrepentant sin. This glorification is explained either by saying that it makes the blessed in heaven more grateful for their salvation, or by saying that it is intrinsically good for God to display his wrath as well as his mercy. I find both of these responses perverse in the extreme. But maybe that's just because I suffer from a bad case of Calvin Derangement Syndrome.
Of course, the Calvinist can also say that this is all part of God's secret will, so of course we have no idea why He does it.