It sounds like you already understand that FLAC and WAV files are mathematically the same, if you convert WAV to FLAC and then back to WAV, the bits will lbe identical.
The conversion can be done in much faster than real time, which is why when you rip a CD, the slowest part is pulling the bits from the CD. My computer can convert dozens of WAV's to any format simultaneously.
Which is my way of saying that given modern computing equipment even in streamers (which will probably have dedicated hardware to do the conversion), it’s trivial to convert from FLAC and will have no effect on sound quality.