Expecting the hash of the WAV and FLAC to match is like expecting the hash of a word document and a LibreOffice document to match; even though they may have the same user content they're two completely different formats.
I don't know enough about the wav format to know why your original wav and the converted wav didn't match, but if you used the same tool and options they should. I converted from a single wav multiple times to wav and flac formats, and all the wav's matched as did all the flac's.
Flac stores the hash of the decoded audio content internally, so even if you'd made lots of tag changes, or even changed the flac compression level itself, it's trivial to compare/validate that the audio is still the same (by storing the original value somewhere).
To display the MD5 of the decoded audio data:
Code:
metaflac --show-md5sum <filename>
To verify that the actual audio data still matches the stored hash (to highlight data corruption):