As far as I know, the current LibUSB support USB 3.0 SuperSpeed. So you should be able to use the FX3 on Linux. On Windows we use the WinUSB generic driver with the FX2 and this driver works very well with the FX3 too, speed is also up to 320MB/s. The WinUSB driver makes no difference between USB 2.0 and USB 3.0 as it is abstracted to the host stack.
I've used the LibUSB driver with the FX3 and while this is within the Windows OS the same driver will work on Linux.
Could you provide some speed test results under Linux? I only get about 70MBytes/s using Auto_Bulk_Loop firmware. I think it's too slow.
I'm using LibUSB 1.0, Ubuntu & Arch Linux 32Bits/64Bits. And It seems Linux has limited support of burst mode and iso transfer.