I'm more sympathetic to innovative monetary policies than most people that have studied the topic, but the monetary base isn't a money tree and unfortunately virtually every claim you've made is false.
The M2 growth figures are available and published by Fed sources. They're nowhere near enough to underwrite a basic income, even if none of that newly created credit was being directed towards useful economic activity
https://research.stlouisfed.org/fred2/series/M2
M2 isn't created by the Fed anyway, it's created by private banks choosing to extend credit to entities they believe are on average productive enough to repay them at prevailing interest rates. It's possible to deter banks from making future loans of course, but I can't imagine doing that to make room for untargeted handouts being a good idea
The monetary base the Fed actually is responsible for issuing is much smaller and has actually shrunk since 2014.
https://research.stlouisfed.org/fred2/series/BASE
QE was a temporary large-scale response to financial shocks which is designed in principle to be reversible so it's about the worst way of funding the steady stream of expenditure required for BI imaginable.
It also consisted of the Fed buying up swapping the cash for existing financial assets in the form of government debt. If they're giving away the newly minted money instead, the amount the Fed can inject into the economy without generating unwanted inflation is much smaller. That might be desirable for a well targeted short term stimulus programme, but a BI certainly doesn't fall into that category (plus you don't get the fringe QE benefit of shrinking the govt debt/interest burden)