Why should we tax consumption as opposed to income or wealth? You claim it's more "fair," but I don't see any particular reason that's the case.
There are three issues here: first, how much does each person "cost" the government? Second, how much should each person pay for that unit of cost, and third, how should we scale that payment?
For the first question, I'd argue that there is a fixed per-person cost, which arises from administrative burden and protection of the body, as well as maintenance of most utilities that we all use roughly equally (roads, etc.). Beyond that, however, most functions of government serve to protect wealth. This includes things like providing a legal system to enforce contracts, prosecute robbery, etc, as well as the general governmental interest in making the economy robust. In real dollar terms, these services benefit those that have lots of wealth more than those with little (notice I say wealth, not income - even if Paris Hilton doesn't earn a dime over the next twenty years, she still benefits from the government's protection of her bank accounts).
This does not argue in favor of a consumption based cost function, but rather a wealth based one, at least once you've covered the "protect my body" utility that we all equally benefit from. An income based cost function gets closer to a wealth based one, but it's still biased quite a bit.
Then we come to the question of how to "charge" for the utility of services that a person receives. Some people think that a dollar is a dollar is a dollar, whether it's taken from Bill Gates, the local fry cook, or the homeless guy that asks you for change; some argue that it's the relative utility of that dollar that should matter, and if we needed to collect a dollar from every person then we should make everyone "hurt" the same to collect that amount of money. That's up for debate, and really comes down to your personal definition of "fair."
But don't delude yourself into thinking that you can label one type of tax fairer than another without defining what you mean by "fair." It's a loaded word that can be interpreted in any of a million ways, many of which are reasonable and defensible but many of which are not. In my opinion, a consumption based flat tax doesn't accurately account for either the burden that each person places on the government, the value of the services they receive, or the personal pain they feel in having to part with a dollar. Feel free to disagree, but do it with a justification.