Please use FX3 Linux SDK instead of USB Serial SDK.
FX3 Linux SDK has support for both FX3 and FX2. You can use the same for FX1 as well.
Please download FX3 SDK from: http://www.cypress.com/documentation/software-and-drivers/ez-usb-fx3-software-development-kit
Thanks for the tip, Keerthy. It seems the device's application uses the CyAPI library. Is there a Linux implementation of that library, or is the source available anywhere? I'm really banging my head against the wall, trying to figure out how I can make this work.