Mountain Lion 10.8.3 file sharing broken for particular named folder
I'm not sure what to tell you about the actual problem but I can share some insight that might help you track it down.  The iMac connecting to the lower case "flac" share but mounting it as "flac-1" tells me it's all ready connected to a volume named some form of flac.  It could just be that it's all ready connected to the SMB NAS you mentioned. 

Regardless I've seen an issue where software expects a certain path and instead of throwing an error about not finding the path it just tried to create it which then leaves a sort of null path that you have to manually remove.  If you don't remove it then names like "flac-1" start appearing.  Re-reading that it may not make sense but regardless the steps I've used to see what's what are firing up Terminal (found in /Applications/Utilities) and typing:

ls -la /Volumes


If you see more listed here than you expect or can find through normal finder navigation then you can remove them (Only do this if you're 100% sure it's a path that contains nothing you ever want to see again!) by typing:

rm -rf /Volumes/NULLPATH


where NULLPATH is what you wan to get rid of.

Along these lines if the mini is all ready showing a "FLAC" or some such in /Volumes then you're not goign to be able to share a folder by the same name.  As in if the mini is connected to the SMB NAS then you're going to have to use a different share name.

Also you can turn ownership on, on your external HD by opening the get info window on the drive and checking the box at the bottom of the window to "Enable Ownership on this volume".  I'm not sue it will in any way effect your issue but might be something to try.