I searched and saw the SNES Classic post about Prime Now availability, but I did not see anything about NES Classic availability (and if you search for just SNES Classic you wouldn't see it...).
In the Prime Now App, In my zip code (a Charlotte, NC one) the NES Classic is currently available in addition to the SNES Classic. Just search for NES Classic and it comes up with the SNES Classic being in stock and available to order as well (as of 8:30am). I have no idea if the URL I input will work for PrimeNow product, but will attempt anyway.
Just went OOS in the Charlotte zip code I made in the post. I know at least one other market got it from a friend, so it may be out in others still, not sure.