it probably won't get you much. I did an experiment where the residual was calculated from a 32-bit float kernel (i.e. no quantization), while still transmitting the quantized coefficients. (of course this file would not decode but it was meant to find the limit for transmitting the kernel.) size improved less than 0.1% in all cases.
FLAC uses low order (<=32) filters so optimizing the size of the kernel doesn't help much. and the simple quantization scheme it uses is already very close in error to unquantized kernels.
you can calculate the # of bits used for the kernel by running 'flac --analyze' on a file, then for each subframe calculate 4+5+order*qlp_coeff_precision, and add up for all subframes. see
http://flac.sourceforge.net/format.html#subframe_lpcJosh
edit: to get the total residual size is more complicated, you have to subtract off the frame header size, frame footer size, subframe headers, and metadata, all calculated from the analyze output.