This is a concern I have as well; if everyone has the same income, nobody has? I'm afraid it would just bump inflation by an X amount. If everyone's base income goes up by 10% due to basic income, wouldn't that just be offset by prices going up 10% because everyone can afford that 10% anyway?
Plus, housing prices are already ridiculous and still climbing; it's at a point now where people need an income in addition to their normal wages to be able to get a house.
It depends if the market is demand-side or supply-side constrained. If everyone had more money and wanted a new TV, TV manufacturers would just spin up production to meet demand over time. If everyone needs a house and housing is restricted by zoning then the price will go up.
One reason basic income might sidestep the housing issue is that unlike city jobs, if a basic income is portable then it makes it easier to avoid living in the city, reducing competition for housing. That's also a good reason against making the basic income dependent on location (e.g. you get paid more in NYC than Reno), since that would just incentivize people to flock to cities.
Also if that seems hand wave-y to you, consider that in Alaska when the oil money goes out, stores usually have sales, lowering their prices to compete for customers.
Plus, housing prices are already ridiculous and still climbing; it's at a point now where people need an income in addition to their normal wages to be able to get a house.