That isn't even strictly necessary. There is a difference between a "flat tax" (e.g. everyone pays 20%) and a "flat fee" (e.g. everyone pays $10,000). A UBI funded by a flat tax is completely unproblematic. People who make $80,000 pay $16,000 and this makes up the difference for the people who make $20,000 and pay $4,000 when they each get a $10,000 UBI.