That's odd. Could you let us know the Spotify version you're currently using? Also, can you try to remove your local files sources at Preferences > Local Files and then sync them again with the steps here?
Same thing is happeneing to me. I recorded my own album and wanted to be able to play it in spotify with the rest of my music. I embeded album art and updated all the track info. When I go to play these local files on my laptop it all shows up fine, but it's when I sync them and try to play these tracks on moble that the cover art won't show. I've been googling the problem for several hours now and have found absolutely no solution. I've found that this problem dates back at least to March 2012 (and I don't even know when Spotify launched) and STILL hasn't been fixed (which I think is ridiculous). I just wanna see my album cover when I play a track. I'm PAYING for this service the least it could do is work right and not have a 5 year old glitch in it.
Lol this is still an issue. The album art loads fine when I view all the songs as an album/playlist. When I play the individual song, no album art. Hilarious that this issue has gone on for so long. Sort it out, I'm sure its not complicated.