apple wallet

Not all store reward cards are supported in Apple Wallet. Check with Kroger to see if their card is supported. They can tell you. Double check to make sure you are trying to add the card in the correct manner, Add and manage passes in Wallet on iPhone - Apple Support

If it is not letting you add it and you are seeing an error, you need to check with Kroger. The steps for adding it are in the support link I provided. If you are following those steps and still receive an error, then it isn't an issue at Kroger's end.

The link I provided you explains how to add passes. If that does not work for Kroger, again, you need to contact them about the problem. They must have some method for you to add the card, since it is not a credit card. Do they have a Kroger app and do you have that app. I'd guess you add it to the Kroger app and that has some method to add it to Wallet, one of the methods listed in the support link I provided.