Yes, CYUSB3014 Supports Linux.
There is no separate driver for Linux. It works with default Libusb driver.
Install the FX3 SDK for Linux available at the following link: http://www.cypress.com/documentation/software-and-drivers/ez-usb-fx3-software-development-kit
Cypress has developed a wrapper using the LibUSB driver, which can be used to develop host applications in a Linux environment.