For a consumption tax, you don't have to track people's purchases. Instead, you track people's sales and the tax is collected by the seller.
In terms of privacy, this is much better, as you pretty much already know that Widget Corp. is a seller of Widgets and the government doesn't need to collect exactly _who_ they sold widgets to, just how much they sold them all for.
In terms of tracking, 90% of the States currently already track sales. It's how they collect State-level sales taxes. Piggybacking on an existing system is much cheaper/easier than running a completely different system, which is why most States currently piggy-back on the federal system for their income taxes.
In terms of black markets, even income made on the black market (currently untaxed due to the income tax system) gets taxed when used to consume things.
As for cheating, it's relatively simple to catch businesses cheating and they already have the structure and the . For the most part, individuals can't cheat because they're the buyers, not the sellers. You may get some used-market under the table cheating, but you can either call that a recycling incentive, or else create monetary incentives to catch it, i.e. a reward (no penalties) to any buyer who turns in a seller who sold them something without charging the tax.