BI won't increase average income, it'll simply redistribute income from the top down to the bottom so the average will stay the same. BI will reduce income for those at the top as their taxes will go up much more than they'll get back in BI. BI will increase income for those on the margin, not across the board, so the market rates simply can't go up across the board, BI isn't creating new money and thus won't cause general across the board inflation.
Ideally BI doesn't come from an inflated money supply, but if the money-holders refuse to pay taxes, where's it gonna come from? I have a feeling that unless the architects of BI can tack that point to the legislation, it's gonna be a glossed over in the dysfunctional halls of government. "The left" will take on more government debt out of necessity to keep society functioning, while dysfunctional elements of "the right" take on government debt seemingly out of contempt for big government...
BI can't just come from inflating the money supply, it wouldn't function if it were implemented that way. BI has to be funded by taxes, and money-holders can't refuse to pay, taxes don't work that way.