Apples and oranges: millionaires would pay no tax on income, but would pay the full tax the moment the income is applied to consumption -- so sure, they could accumulate wealth untaxed, but in order to enjoy it rather than just stare at it (in theory -- see below), they'd have to pay the full rate. It doesn't seem very relevant to compare progressivity of income in preference to consumption.

With that said, the FairTax is bad for other reasons -- by concentrating all your taxation on something that's relatively easy to hide, you massively increase regulatory and compliance costs. Imagine the blooming industry in recharacterizing consumption purchases as investment purchases! (For the rich, "sufficiently advanced investment is indistinguishable from consumption".)