If I understand your process, you multiplied US GDP by average tax burden, which makes sense, but here's another source that added other sources up: http://www.usgovernmentrevenue.com/total_revenue_2015USrn and got ~6,500 billon USD for USA Revenue. Using the same military budget, that makes = 7.69% of tax on military budget.

I think I see why everyone uses GDP: tax revenue is difficult to calculate, especially when it involves 50 states and a few territories.