Given how difficult Kant is to read and interpret, perhaps we can cut Rand some slack on this issue. Shoshana Milgram, however, does not believe Rand requires any slack cutting. While she admits that there is no evidence that Rand read Kant, she contends quite laboriously that Rand had too much intellectual integrity not to have read Kant. What about those of us who are inclined to suspect that Rand did not read Kant (or read very little of him)? To such skeptics, Milgram has this to say: "To go as far as to say [Rand] didn't read any of these guys [like Kant] ... you don't have the evidence for that. And you need evidence for it." This is an example of what Rand apologists frequently will do when faced with criticism of Rand. They attempt to hold Rand's critics to a higher standard than they are willing to follow themselves. For the fact is, Milgram does not provide any evidence that Rand read Kant. Why does she demand from Rand's critics what she herself is unwilling (or unable) to provide?
Be that as it may, over at quora.com I've tackled a related issue, namely: Why did Rand refer to Kant as the most evil man in mankind's history? Here's my answer to that question:
The ostensible reason why Rand referred to Kant as “the most evil man in mankind’s history” is she believed that, more than any other philosopher, Kant “closed the door of philosophy to reason.” Why Rand believed this is a bit more complicated. It’s important to note that Rand’s views on Kant are, to say the least, controversial, and no Kantian or Kant scholar would agree with them. The idea that Kant’s philosophy, particularly The Critique of Pure Reason, constituted an attack on human knowledge and reason was first popularized in America by George Santayana in his book Reason in Common Sense. “Side by side with this reinstatement of reason, however, which was not absent from Kant's system in its critical phase and in its application to science, there lurked in his substitution of faith for knowledge another and sinister intention,” wrote Santayana. “He wished to blast as insignificant, because ‘subjective,’ the whole structure of human intelligence, with all the lessons of experience and all the triumphs of human skill, and to attach absolute validity instead to certain echoes of his rigoristic religious education.” In the first few decades of the twentieth century, Santayana’s view of Kant and other German philosophers enjoyed some measure of influence among conservative intellectuals in America. This is where Rand seems to have picked it up. Perhaps the most important influence in Rand’s philosophical and political development was the conservative novelist and literary critic Isabel Paterson. According to one of Rand’s biographers, Jennifer Burns (who learned this piece information from the Rand archives), it was from Paterson that Rand probably derived her view of Kant.
With all this in mind, we can advance a more plausible conjecture of the real (as opposed to ostensible) reason for Rand’s colossal disdain for Kant. She needed a scapegoat, someone to blame for why people immediate accept her philosophy Objectivism philosophy of “reason,” egoism, and laissez-faire capitalism. Since she had already come to believe, for reasons which neither she nor her acolytes have adequately elucidated, that philosophical ideas determine the course of history, it was only natural that she would need a philosophy—or a philosopher—to blame for the events and trends in the course of history which she detested. With Paterson as the initial inspiration, she chose Kant.