I have a Model 637-2. It has the coating too. I wouldn't say it is flaking. It is more like it is just wearing off in places. I pocket carry it. It hasn't bothered me. It is just cosmetic, it doesn't effect the functioning of the gun.
(Luke 11:21 KJV) When a strong man armed keepeth his palace, his goods are in peace:
(Luke 22:36 KJV) Then said he unto them, But now, he that hath a purse, let him take it, and likewise his scrip: and he that hath no sword, let him sell his garment, and buy one.