I admit I don't quite follow your connectivity steps for playback but yes, you can use a Mini to make and store flac files. Depending on what device you are using, you can either set up a folder to be shared or use an application that shows your collection in a DLNA set up.
You may want to check out XBMC, PLEX and JRivers for some playback option software.
I have a fair size CD library converted to both Apple Lossless and also to flac. The former is for my portable music playback and the latter is for my home theater set up (AVR receiver and nice speakers). I store my flac on a NAS and it is recognized due to an installed app as a DLNA recognizable system so that my receiver can see it. My receiver also has an iPad/iPhone app that works very well to access the files. Also, my Oppo 103 blu ray player can see those files as well.
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Mac Mini, Marantz NR1602, Goldenear 5.0 system (left and right are Trition 7), 2 x QNAP NAS, Oppo 103.