I can't seem to find a NAS solution, aside from a custom built one, that is able to stream FLAC audio via UPnP. Streaming seems to be limited to MP3 or other popular formats. Do any exist that will stream FLAC, or maybe transcode to MP3 and stream?
From your question, it sounds like you are looking for a UPnP-capable backend for streaming FLAC to some unspecified frontend(s) for playback. It also sounds like you're seeking a Network Audio Server "NAS", not a Network Accessible Storage "NAS". This is an important distinction to recognize, because the latter NAS is the traditional usage, and most NAS products are mainly file-servers, not media servers.
The difference, really, is hardware vs. software. Network storage "NAS" is a hardware problem with hardware solutions. Network audio server "NAS" is a software problem with software solutions. I think what you're asking for is a product that provides both.
Frankly, I don't know the product space well enough to suggest anything in particular. There are lots of frontends that claim to support streaming FLAC, either from servers in the same product line or from general network storage "NAS" devices, but not many network audio server products specify streaming FLAC and supporting UPnP. Note that most claims of "streaming FLAC" are just marketing-speak for "plays FLAC files from network share".
Any network storage "NAS" devices will support FLAC -- all they're doing is sharing files. UPnP+FLAC is another matter; since the DLNA standards don't require FLAC, it is up to the hardware manufacturer to provide or the end user to add on support. Any hardware NAS product that runs Windows Home Server (or even FreeNAS, as Molly suggests) can run network audio "NAS" software as an add-on.
FLAC's homepage and Hardware links page is a good source of information on FLAC-capable products. See also the Hardware support section of Wikipedia's FLAC article. Most of these will be frontend products capable of decoding FLAC formats, but some manufacturers may include backends in their product lines.
Realistically, I don't think anything will be fully plug-n-play in the way that you want. But a Windows Home Server product, possibly with add-on media server software like Asset UPnP (or even XBMC/TVersity/Boxee or similar), may fit your bill for a NAS+NAS backend. I hope some of this info helps.
The QNAP NMP-1000 looks like an awesome NAS/multimedia player.
One of its many features is: