Without intending to be too kind, the question this book really raises is who should read it. Some will love it while others will hate it. What will be your reaction?
Flattery is one of those subjects that most people cannot and do not want to take seriously. If you like a little humor with your social commentaries, you will enjoy this book.
If you want a how-to book on being a more successful flatterer, you will find some helpful hints towards the end of the book. But you will feel unrewarded by the histories of flattery, beginning with studies of chimpanzee behavior.
If you want to learn how to defend yourself against flattery's corrupting influences, there are useful ideas here and there. But you will probably still feel vulnerable in this regard ( . . . at least until someone praises you for avoiding being taken in by flattery . . . assuming the praise is genuine, and not just flattery).
If you want a guide for how to praise, rather than flatter, you will find some ideas here. But that's also not the book's purpose. You belong elsewhere to serve your purpose.
If you take a very reverent attitude towards the Old Testament, you may be offended by what the author has to say about God in that context. You should skip at least that chapter or perhaps the entire book. If you are an agnostic or an atheist, you should probably start there in chapter three.
If you have read widely on flattery (animal experiments about how "alpha" males are created, Machiavelli, Castiglione, Franklin, Bacon, Dale Carnegie, Chesterfield, and troubadour verse), you will find little new in this book except for the quips. Now, the quips are quite good, so you may like the book anyway. But be aware that about eighty percent of the book is providing such historical perspectives.
On the other hand, if you want to add to your repertoire of cocktail party stories, this book is excellent. You get humorous glimpses into the foibles and virtues of those who wrote about flattery, as well as their writing. Mr. Stengel is a witty story teller, who makes it all much more interesting than it really is. For example, anyone who likes Dale Carnegie books or courses should read about Mr. Carnegie's background as an unpopular young person and ineffective salesman.
There are many legitimate ways to attract attention from people that are different from flattery (in the sense of "false praise"). For example, you can simply be very attentive because you respect all other people. You can tell funny stories because you like to amuse. You can help people accomplish things they care about, because you like to make life better for others.
Whatever you do, be sure that you choose how you want to be sociable, however, rather than simply falling into the habits of flattery without thinking about what you are doing. The unconscious desire to please may take you along paths you don't really want to trod.
Have true friends and a meaningful life!