FLAC is a lossless compression. When a FLAC file is decompressed and decoded during playback, the digital result that is fed to the D/A converter and audio amplifier is identical to the source.
M4A (AAC) is lossy compression. The decompressed and decoded digital data is not the same as the original source file. However, the compression algorithm is very sophisticated, and the idea is that the difference should not be perceived.
Whether you can hear the difference between the original source (or lossless-compressed version) vs. a lossy-compressed version like M4A depends on several factors: 1) The quality of the original source, 2) How good your ears are, and 3) The listening environment.
In any case, there are only two possibilities: 1) You cannot tell the difference between the FLAC and the M4A, or 2) The FLAC will sound better. In no case can the M4A file sound better than the FLAC, given the same source file.
In your specific situation, given that your source is already lossy-compressed (from Apple Music or Spotify), consider: You do not have a high enough quality file to make FLAC worth the extra disk space. Remember that FLAC is lossless, so if you store the file as FLAC, then when decompressed and decoded, what you have is a file identical to what was originally downloaded from Apple Music or Spotify, which itself is lossy-compressed. Storing the original downloaded file on your USB drive and playing it directly will play it back identically to the FLAC at 1/5th the disk space.
FLAC is really only useful when you have an original, uncompressed source, e.g. directly ripped from CD (PCM), Super Audio CD (PCM), DVD (if the audio is PCM, which is rare), or Blu-Ray (if the file on the Blu-Ray is also lossless: PCM, DTS-MA, Dolby TrueHD). In those cases, FLAC can preserve the original uncompressed audio at about half the disk space.
For any other source, which is likely already lossy-compressed, then using the original file is best rather than reencoding to anything else.