FLAC is the literally the dumbest thing ever

Prove to whom, why and how?

First you claim there's no audible difference between lossy and lossless formats, then you do an about-face and claim you can hear it. So, which one is it? Choose your master!

I don't see the sense in proving it, and whom you'd want to prove it to as the one and only person mattering in how you store your music is: you.

Proving it is easy enough, though, as lossy compression employs psychoacoustic masking, which is always designed to accommodate an ideal average listener, which means it will produce acceptable quality for most real listeners, but perfect quality for no real listener. Furthermore, the masking model is always optimized against a limited set of reference samples, which can never do the real-world range of acoustics justice. These facts alone provide ample theoretical proof that lossy and lossless compression will inevitably never sound exactly the same.

As for practical proof, book a sound proof room with reference equipment and a staff of independent experts and do a double-blind test on a sizable set of samples extracted both from music you habitually consume as well as reference audio (such as the infamous EBU V3/SQAM), and you will soon hold your proof in hand - whatever good it may do you.