Can Apple Lossless audio files (ALAC) be converted to FLAC audio files with no loss of fidelity?
Yes, given that both are mathematically lossless, conversion is lossless too.
The reason for this is that the signal can always be reconstructed to its original form when a FLAC/ALAC file is decoded. Thus, they are equivalent and you should experience no loss when transcoding — even when transcoding multiple times.
The only error I could imagine would be an arithmetical one, e.g. through limited floating point precision in calculations. I don't think this applies to either FLAC or ALAC.
In case you only use a "psychoacoustically" lossless codec, this is not possible. Lossless in a psychoacoustic sense would mean that you can't distinguish the original and the compressed version, yet they are very different from each other. MP3 or MPEG-4 AAC use various psychoacoustic techniques to achieve this. Thus, when transcoding, the original version can't be reconstructed and you'd experience a loss of quality.
In case you want to convert ALAC to FLAC,
FFmpeg will read ALAC without issues. For *nix systems, there's also a script called Convert to FLAC which makes the whole process easier. With Bash you could simply convert all files in a single directory as well:
Note: If you get a message about
If you have a Mac (since you have ALAC files), you could also use the open source software Max as nice frontend to do the conversion from and to ALAC/FLAC or many other formats..