The way to do this is to get the HDX to convert the files from WAV to FLAC first. Assuming you are using a PC, you can load on the Windows Desk Top Client which you can download from Naim's website. The software isn't terribly intuitive and feels like something from a computer museum but you can probably work it out, or if you post back here, someone with more knowledge than me will tell you exactly what to do. But basically there is a convert option that you set and it will do it in the background, which may take a while if you have a lot of music.
Then having converted the files, you can save them to your NAS either by backing up from the HDX to the NAS or by copying and pasting directly from the HDX to the NAS.
The reason for doing the conversion in the HDX is that Naim uses a proprietary way of storing metadata in WAV and if you just transfer the WAV files, you will run into all manner of metadata issues which will potentially take a lot of work to sort out. This doesn't happen with FLAC.
When you change your NAS, you put them both on line on your home network and then you can copy the files over by copying and pasting or drag and drop or whatever. I would copy rather than move because if anything goes wrong you still have the original intact.
Then you set your upnp server on your NAS to convert from FLAC to WAV on the fly as it serves a file, if you are worried that you can hear the loss of sound quality caused by the Naim unit having to work harder to play a FLAC directly.
best
David