Use an audio shield or MP3-player module. There are some insanely cheap MP3 player modules on ebay (like, cheaper than a cup of coffee) - they all take an SD card (or more frequently micro SD card). This is the correct way to play sound files under control of an arduino.
Using a thumb drive for storage on an Arduino is possible, but you need a USB host board (which costs more than an arduino from the same supplier, eg, 30+ from adafruit/$parkfun, 5+ on ebay), and interfacing with them is resource intensive and awkward. USB host on a microcontroller is awkward, expensive, and except for very common USB devices (HID, mass storage, that kind of thing) with generic interfaces, often hard/impossible to make work because you need drivers, which are only provided for the major OS's. So if you wanted something exotic, you'd need to write your own driver, which would require information that the manufacturer may not make available. But in any case, even once you get the sound file off the thumb drive, it's hard to turn that into sound on an Arduino with acceptable fidelity. So what I'm saying is, host shields exist to interface with USB devices that are meant to plug into a computer - but they are expensive and hard to use and almost never the right tool for the job. And generating decent-quality sound from an Arduino is hard too.