Many UBI methods are combined with a flat tax. One way of phasing it in (which is almost certainly going to be necessary, as a straight jump to a full UBI would be disruptive) would be to start off small (say, $100/month distributed), funded entirely by a very small flat tax.
The UBI itself would never be taxed itself, nor counted as income for setting tax brackets. The amount that is taken out by the flat tax is also not not reportable as income. The tax rate itself would set to be be exactly what's needed to cover the payments, and would be on corporate profits, personal income, and as an added VAT, all at the same rate.
You could distribute $100/month ($1200/year) for about a 1.8% flat tax/VAT rate while leaving everything else alone, then adjust other spending (and thus the need for other taxes) as the UBI increasingly reduces the need for other services. You can also start to adjust minimum wage rates as the UBI increases (e.g. by around $0.50/hour for each $100/month of UBI being distributed, delayed by a year).
So, at $1,000/month, you'd be at around 18%, $2,000/month ($24,000/year) around 36%. At that rate, if you're making less than $70,000/year, you would be receiving as much in UBI payments as you're paying in salary. You'd also be paying more for purchased items because of the VAT, but that's before taking into account lower additional taxes (that you currently already pay) as the government reduces costs of other programs, reduced prices of good through the reduction in minimum wage, etc. Some of that reduction would be automatic as your reportable income (and tax bracket) go down as the flat tax increases.
I'd like to see the elimination of capital gains tax because the budget of the country shouldn't depend on the whims of the market. You'd also eliminate the primary means of gaming the tax system. Instead, add a very small transaction tax (0.05% - 0.1%, perhaps.
With a flat tax system, you eliminate most deductions. Instead, use direct subsidies for things we want to encourage (e.g. subsidize lower interest rates on home mortgages, but only up to a certain amount for the loan). For charitible contributions, make direct matching funds (e.g. at 20% of total contributions) instead of giving tax deductions, meaning contributions from rich people are no longer being subsidized by everyone else, everyone's contributions are as valuable regardless of how much money you make. The VAT rate could be made lower for food and medicine and other basic necessities. Much more directly subsidizing things would be better than our current indirect subsidy through income tax policy where your subsidy is higher the richer you are.
You'd still need additional mechanisms - Universal Healthcare would still need to exist (and could be the primary solution for almost all circumstances beyond the norm, whether mental or physical needs). You wouldn't eliminate Social Security, you'd phase it out over time (people who have paid into it for their entire lives shouldn't just lose it arbitrarily). Inexpensive education (including online) and communication (computers and internet), affordable housing, public transportation, there are still many things that we'd want to have government doing.
$24,000/year seems to me a reasonable goal. Most people want a significantly higher standard of living than that will provide, so there's still plenty of motivation to do something useful, with no disincentives to making additional money. Rich people don't say "hey, I have plenty, I'm going to stop trying to make more money" - if having $24,000/year was enough to keep people from working, they'd already be doing it, there are plenty of people with a couple million in assets that could just kick back and live the grand dream of surviving on $24,000/year.