It's a legitimate criticism, but he's arguing a strawman.
First off, the reviewer's coinflip analogy is deeply flawed. If you take a million draws from a binomial distribution, it's not going to end up the same as a million draws from an exponential distribution. That has an even deeper meaning when you, as an individual, are one random draw from said distribution, especially if you want to live in a society that considers itself "fair" (whatever that may mean).
Now Frank is not arguing against inequality. Frank is an economist, and almost no serious economist is against inequality as a whole concept (though many are against extreme inequality and, importantly, social immobility) because inequality is what you'd call "incentive compatible".
Frank's policy proposal is consistent and sane, but it will rub some the wrong way, as any policy proposal does. I'm certainly in favor of it; consumption is a better target for progressive taxation than most of what has been proposed this election season. That's the part that got the reviewer so riled up. I'm guessing the reviewer is not a professional economist.
The idea of a progressive consumption tax is consistent with microeconomic theory, too. People value things in an ordinal (not cardinal) manner, and at a sufficiently high level of income this means consumption has to be conspicuous to some degree (that's Veblen's whole insight).
Of course, political feasibility of the policy proposal is one thing, and certainly many worse policies are more politically feasible, as exemplified by how rubbed that reviewer has been by Frank's book.
The main difference between this book and Taleb's book is that Franks book is "Successful people are lucky, here's a policy proposal" and Taleb's book is "Successful people are lucky and also everyone is dumb and I'm so smart"