It takes however long MyPoints usually takes to process the reward. I don't recall it being instant, but it wasn't 6-8 weeks like some programs. The Amazon claim code should come as an email, not via snail mail, but it has been so long since I redeemed that I cannot say 100% that it was/was not within 48 hours.
Sorry if that isn't too helpful, but I really don't recall it being instant receipt upon redemption.
The instant code is instant! I just redeemed points for 2 of them on BF and was worried it would take a day or two. Nope, I redeemed, checked my email and they were there