I've personally had cashback approval in less than a 2 weeks for Amazon.
Yes, these timeframe are quite an annoyance, especially the travel ones where it may take up to 150days, but at the end of the day, it is free money. And I do forget about it most of the time only to check my balance one day and find I got $50 withdrawal. Its a good feeling.
CRW Price at posting:
$1.76 Sentiment: Buy Disclosure: Held