Instead of faxing everything in and hoping for the best, call the number on the kroger gift card receipt!!
If infact it wasn't activated correctly, they will be able to resend the activation signal and activate it for you instantaneously over the phone. If instead there was an attempted use on the card before you purchased it (VERY common), they will be unable to activate it for you, but they will give you a case number and tell you to go into the store and at the store they will be able to give you a new giftcard. Just did this the other day for two cards and within an hour everything was fixed.