> How does UBI even work? Won't it just lead to rampant inflation where the basic income is spread thin, eaten up almost entirely by the rising cost of goods?

In the long run UBI promotes innovation and competition. Therefore those industries with competition would not suffer from rampant inflation.

Businesses without competition (monopolies) would on the other hand experience huge inflation simply because there is no pressure to keep the price down. This would be the case of natural monopolies (eg. banks or networks such as telecommunication, railroads, water systems) and government guaranteed monopolies (pharma, US healthcare, various overregulated industries).