If you want to merge the UBI into "tax terminology" you could call it a "refundable tax credit" - as a refundable credit it still gets paid to every person, whether they pay taxes or not. Putting UBI into that context may fit better with the existing gears and levers of our tax collection/payment system.
The UBI component makes your "flat tax" into a mildly progressive tax. I don't mind that, but I do think we ought to have a heavier, or "more progressive" tax load on high incomes (or for that matter on high collections of wealth [whether that wealth is directly owned or farmed out via a mesh of US and foreign corporations and trusts.)
