Quick questions regarding adpcm .wav files.

I know these files are lossy but is it best to compress them using a lossy codec like mp3 or a lossless codec like FLAC?

Storage space isn't a problem but would transcoding an already lossy file to mp3@320kbps affect the quality much or should I compress with the FLAC codec to be sure?

Yes, ADPCM is a lossy codec. That much is correct.

The nature of ADPCM is miles away from current lossy codecs, as to say that adpcm is more similar to lossywav than to mp3. This difference is key here, because it implies two things:

It may be easier to encode for a lossless codec, than the original signal it originated from. (That depends a bit on the lossless implementation, if it can gain from the more predictable signal it has).
Another lossy codec (mp3-like lossy) shouldn't find this signal much different than an original.(it hasn't been "transformed"). Also, due to the nature of ADPCM, 320kbps may be too much even. Try using an VBR setting ( start trying with -V2 ).
Since there are no artifacts (in the lossy sense) to try to hide, the encoder itself won't amplify them.

Thanks for clearing that up and for the quick response