i've used foobar via sox to do this a number of times without issue -- in fact, I now simply track out my 24/96 masters and use foobar resample presets to resample/dither to 16/44.1 when I need to burn a cd, or 24/48 apple lossless when I want to listen on my iPhone.
If you use apple devices to play music, you might want to consider resampling your stuff to 24/48 apple lossless instead of flac to save the extra step. You'll need to dig a bit deeper to learn how to set this up, but it's not too difficult.
Finally, what squeezebox version are you using? I thought the more recent squeezebox touch played 24/96 without issue