My assumption is that the wealthy do not consume in proportion to their income -- so someone who makes 10x as much money as a poorer person likely only consumes, say, twice as much. Redistributing some money to the poor would not cause the wealthy person to decrease their demand for goods as much as it would make the poor person to increase their demand.
Everything that is consumed must first be produced. If you're not producing more, a rise in demand will mean a rise in prices until demand matches supply. I think the end result would be that prices would rise, but it would still be a good thing for the poorest citizens to have the ability to buy what they really need, and to have the flexibility to leave toxic work environments without immediately suffering huge consequences in terms of losing a place to live, etc. So while price inflation should be considered, it doesn't mean we should immediately throw out the idea of basic income.
And eventually supply of certain goods would probably increase a bit to match demand better, but it wouldn't completely cancel out the rise in prices.