You could keep it flat up to a high threshold, like top ~5% of salary, then transition to marginal tax

You don't need it, it's already built in. The flat tax rate needed to serve as the implicit benefits phase out is already in the range as what you'd use in the high tax brackets in a progressive tax system with separate benefits phase outs.

If you want it to be more progressive you raise the flat tax rate and use the money to increase the UBI. If you want a less progressive system with lower taxes you do the opposite. Making it needlessly more complicated gains you nothing and costs you efficiency.