I also purchased a $24 Baofeng from Amazon, and then faked up a cable and got it to communicate with CHIRP under Linux. I think I made every possible mistake first, so after you are sure Linux has recognized your USB cable, check the following:
1) Push the plugs in to the radio really hard. If there is still an air gap, it's not in far enough
2) Tune the radio to an unused channel and set the squelch. Apparently, the serial signal on the cable is shared with the speaker signal.
3) turn the volume all the way up. (see 2 above).
I found these instructions in the CHIRP setup messages for the radio.
My faked cable simply connects the 3.3V serial port TxD and RxD from my Raspberry Pi GPIO via 2k resistors, and GND, to the proper plug pins on the Baofeng: no USB at all. This works because Baofeng uses 3.3V serial. This is NOT a serial standard but has become a de facto standard for modern CMOS direct serial connections. In addition to converting USB to serial, a programming cable also converts to the proper voltages plug pinouts for the specific radios the cable is specified for.