I have no interest in Flew's past, so I skipped to start at Chapter 4 where he laid the cards on the table. He saw three important scientific spotlights 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.
I don't claim myself to be a philosopher, but I do understand that philosopher thinks deep and looks at things from multiple view points to try to draw a reasoned conclusion. However, with the cards laid as such, I saw an immediate problem.
Let me just deal with the first "card" in this post.
Laws, in this case, refers to the physical laws, e.g. theory of relativity, energy and mass conservation and so on. We must understand that these "laws" represent our human collective understanding of the Universe around us. Nobody writes the laws and then get nature to "fit into the laws". Human observes, from the chaos around us, we apply reasoning and logic, to explain repetitive occurrences of events. There are events which cannot be verifiably repeated and such events do not fall into the science realm. As such, no wonder nature obeys laws BECAUSE the laws are the ways we describe the nature.
In Chapter 5, Flew continued his flawed argument asking the question who wrote the laws.
Yes, many physical laws are beautifully symmetric when expressed in the mathematical equations, sometime is also simple beyond belief. However, mathematical formulae are shorthands. For the uninitiated, each of the symbols in the formulae can take books just to explain. For the physicists and mathematicians, the symmetry expresses the "regularity" or the consistencies of repetitive events. The simplicity on the other hand reflects the deep levels of abstraction the mathematics as a tool has. Combined, that represents the expressiveness of the tools we human used to describe the regularity of the Universe.
Taking the hint from Flew, a more philosophically worthwhile question may be "why nature exhibits consistency and hence we can observe and create laws to explain/predict similar events". But asking the "why" question is dumb, as explained by Richard Dawkins. Purpose, as the question behind the why questions, is a human mind construct. We constantly need to simplify all the chaotic happenings around us and our minds organise them into causal relationships, evolutionarily that help us prepare to respond to potentially deadly events.
I'll respond to the next two "cards" after I read the corresponding chapters.