In some soundtracks, the producer would put in a dialogue preluding the actual score.

Example: Pulp Fiction - Misirlou

Though I want to skip the dialogue, I don't want to actually delete it from the FLAC file
since I want to retain its "mint" condition.

After remembering that some WAV files had looping cues that are used for game music,
I wonder if FLAC has a feature where by adding a non-destructive metadata, a music
player e.g. Winamp will always play the edited track where I set the "starting point."
So for Misirlou, I would set the starting point at 0:14, and every time I play that file it'll
play only the music part.

You can insert INDEX points, either in FLAC's special CUESHEET metadata block, or in an external cue sheet, but every player I know of will play all audio sequentially. Making the start of the file (dialog) INDEX 00 and the start of the music INDEX 01 will only help if you start playback with the song in question, i.e. if it's not part of a larger playlist (the songs before it).

I think the most effective solution would be to cut the songs in two, with for instance "01.00 - dialog.flac" and "01.01 - music.flac", and use a custom playlist for playback, including only the files containing music (leaving "01.00 - dialog.flac" and such out of it). It would still be lossless.

I will use the splitting method, thanks for the suggestion, skamp.