Another option if you don't mind the player being a little bulky is to get hold of a 2nd hand handheld Sat Nav GPS with a headphones socket and runs on Windows CE Core edition (most brands apart form Garmin and TomTom do). A model with SDHC support would be better due to the size of FLAC files. A lot of Sat Nav manufacturers don't provide updated maps for their older devices, so some people end up buying a new Sat Nav for updated maps and likely have their old Sav Nav device lying around that they wouldn't mind selling off for very little.
With most Sat Nav's that run the WinCE more, it is possible to kill the running navigation software by replacing the navigation software executable with something that acts as a task manager/killer (e.g. WolfToolbar), which leaves you with the Windows CE GUI shell. Do some research first, as like using unofficial firmware, there are a few Sat Nav models can be "bricked" if the wrong files are tampered with, not to mention voiding any warranty that may be left on the device.
Once in the WinCE GUI, all you need is a WinCE compatible media player (e.g. the freeware HPC Media Player), which will play a wide variety of audio and video files, including FLAC, OGG Vorbis, Musepack (MPC), AAC, Dolby Digital (AC3), etc., not to mention a wide range of video formats.
The following is a snapshot from my own Sat Nav running HPC Media Player with a selection of FLAC encoded tracks: