So I get where you're going with this, but the businesses are still competing with one another in a free market.
So yes, you're right that if all the avocado farmers in California decided to engage in price fixing because they know that more money exists and that they can get it, they probably can. But it presupposes highly monopolistic behavior that doesn't seem very likely to work for most markets. Especially if it's easy to become an entrepreneur.
The business, after all, makes a profit as long as their price is above their cost. So unless their costs go up, competition keeps prices down.
Now, I think you're half right -- prices will go up, but it's not because of gouging by middlemen or traditional inflation. It will be because as people drop out of the labor market, the really undesirable jobs will become more costly to fill.
But that strikes me as a much more fair free market than what we have now. Yes, you will have to pay more to have your garbage picked up in front of your house. Why? Because as it turns out, you would much rather be doing whatever you do than deal with a thousand people's garbage. Maybe they should be getting paid more than you, in a voluntary free market.
So I imagine it will be sort-of inflation, but almost better described as a rebalancing of the economy. Jobs that humans can do much more easily than robots will get higher salaries. Jobs that are enjoyable get lower salaries. Overall, salary spread across jobs becomes much smaller.
But I don't think it's necessarily likely to be some kind of overall inflation, it's a redistribution of wealth accomplished by simultaneous direct transfer of wealth through the UBI, in addition to a redistribution of power accomplished by allowing "Nothing" to be an option that employers have to compete against.