Fringe benefits would not have been deductible by companies under the Armey proposal. Why? Because the proposal chose not to tax such benefits as income at the individual level. Therefore, to assure tax neutrality, namely that all income streams would be taxed, but only once, the stage of taxation would have occurred at the business-level (via non-deductibility of fringe benefits).
As to your calculation wonder how you did that. First of all most flat tax proposals will still have some sort of personal exemption, which would be a large source of debate so what you used here may or may not be right or close to right. Also a flat tax is still a rate, who knows what rate government will use. Lastly circumstances change for any individual. So for example if you were a renter when you calculated, and now own a home then losing the mortgage deduction would make a big change, same with if someone had high medical costs in a year or gave a lot to charity.
People think of deductions as lookholes. Many are. Others are there for social or economic prurposes. Again in the mortgage deduction example. If you or anyone is a homeowner have you included in your calculation the loss in value in your home as mortgages will now be an after tax event versus a before tax item.
Every hard problem i.e. tax revenues has a thousand easy answers, most of which are wrong.