Any commonly available handgun cartridge from .22 Long Rifle up to .500 S&W Magnum can cause permanent hearing damage if fired without hearing protection. While the decibel level of a .38 Special is lower than that of a .357 Magnum (156.3dB vs. 164.3dB) both are well above the threshold (roughly 140dB) to cause pain and permanent hearing damage.
Because of this, the decibel level of my chosen defensive gun is pretty far down on my list of priorities. I simply accept that, if I have to use a gun in self defense, I'll have some permanent hearing damage after the fact if I'm lucky enough to survive the incident. I honestly very highly doubt that, given the limited number of rounds I would fire in self defense (if I have to fire more than a magazine or cylinder full in SD I've got much bigger problems than how loud the gun is), that there would be much difference in terms of hearing loss in the long run. Of course, if you're planning on routinely shooting without hearing protection it's a different story, but I wouldn't recommend that regardless of the caliber.
If you're really that worried about "saving your ears" in a SD encounter, I'd suggest that keeping a set of electronic ear muffs near your HD handgun would go a lot further towards that goal than worrying about the caliber.
As to the flash, that depends a lot on what ammunition you have loaded in the gun. In my experience, .357 Magnum ammo loaded with lighter bullets tends to be "flashier" than that loaded with heavier bullets. Also, the more premium, self-defense oriented lines of ammo (PDX1, Hydra-Shok, Golden Saber, Silvertip, Critical Defense, etc.) is more likely to be loaded with flash suppressed powder. So, if you're using "value line" .357 ammo with 110 or 125gr JHP's then flash might be an issue, but if you're using premium ammo and/or that with 140+gr bullets, it's really no worse than a 9mm +P or .40 S&W in my experience.