As a matter of policy, I'm all for broadening the tax base, ideally to 100%. But that makes zero sense in concert with BI.
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.
One argument I see for making them file anyway is reducing disincentives to work; I'm not at all sure the magnitude of that disincentive is worth the extra paperwork, though.