I think we'd definitely want to count BI as income in general, but we may want to rework the tax code on the low end such that if BI is your only income you don't need to file, as fredkbloggs suggests. One way to do so might be setting the standard deduction equal to BI and eliminating refundable tax credits.

I can also see introducing BI as an opportunity to remove some of the tax expenditures that riddle the tax code -- broaden the tax base. But I don't see any reason to change the basic nature from progressive to flat. After all we'd still need to raise quite a bit of money to pay the BI as well as the remaining government functions that BI doesn't replace. Even under the current progressive model, eliminating tax expenditures is probably not going to be enough.