Here’s an excerpt from the book’s Chapter 4, “The Pilgrimage of Reason” (Page 88-89):
I now believe that the universe was brought into existence by an infinite Intelligence. I believe that this universe’s intricate laws manifest what scientists have called the Mind of God. I believe that life and reproduction originate in a divine Source.
Why do I believe this, given that I expounded and defended atheism for more than a half century? The short answer is this: this is the world picture, as I see it, that has emerged from modern science. Science spotlights three dimensions of nature that point to God. The first is the fact that nature obeys laws. The second is the dimension of life, of intelligently organized and purpose-driven beings, which arose from matter. The third is the very existence of nature. But it is not science alone that has guided me. I have also been helped by a renewed study of the classical philosophical arguments.
My departure from atheism was not occasioned by any new phenomenon or argument. Over the last two decades, my whole framework of thought has been in a state of migration. This was a consequence of my continuing assessment of the evidence of nature. When I finally came to recognize the existence of a God, it was not a paradigm shift, because my paradigm remains, as Plato in his Republic scripted his Socrates to insist: “We must follow the argument wherever it leads.”Flew makes his deistic argument on God at a purely natural level, and he asserts that his discovery of God has been a pilgrimage of reason and not of faith: “I must stress that my discovery of the Divine has proceeded on a purely natural level, without any reference to supernatural phenomena. It has been an exercise in what is traditionally called natural theology. It has had no connection with any of the revealed religions. Nor do I claim to have had any personal experience of God or any experience that may be called supernatural or miraculous. In short, my discovery of the Divine has been a pilgrimage of reason and not of faith.” ~ (Page 93)
There is no doubt that the matter of God and religion continues to be contentious, but I think Flew's There is a God: How the World's Most Notorious Atheist Changed His Mind is a fine book for developing a perspective on philosophical theism.