Track times being misreported + files don't play in Plex Web

Are you certian that these are actually flac files (and not just renamed with a different file name extension)?

Do you have
Settings - Server - Scheduled Tasks - “Upgrade media analysis during maintenance”
enabled? If not, do it.

Have you tried a Plex Dance?

Check with a metadata editor that these flac files only have meta tags in “Vorbis comment” format in them. Don’t use ID3 tags or Ape tags in flac files.