Not if the flat tax is based on yearly income. Putting a flat tax in affect without adjustments for income can't work. To give refunds is, in my opinion, a backassward way of doing a simple job, giving a break to the lower income levels to prevent an outcry of "Carrying the rich". Lets face it, we hear that now even though its not true. The liberal left would have a field day with an unadjusted flat tax, but that shouldn't prevent the adoption of a simple tax.
So in order to cover multiple checks, the individual makes the adjustment, with a calculator by simply keeping a running total and making a quarterly adjustment.