Depends on what you mean by 'current system' (Fed inc tax, all Fed taxes, all taxes?) and flat (flat rate w/ or w/o 'flat' base?). Exemptions, deductions really contradict flatness, strictly speaking. Graduated rates are just inverted phased-out deductions.
The Fed income taxes are progressive. Throw in the payroll tax and the total is still progressive. Include all taxes Federal state and local and the result is said to be more nearly proportional with dips up at the bottom and top (e.g., higher effective rates).
It would be hard to collect the same revenue and achieve greater progressivity with a single-rate tax. You could fantasize about getting rid of all deductions, but that's all it would be.
No way a VAT can be progressive, if you think it is paid by consumers.
mbs