To my knowledge, Kroger has no exclusive arrangement with a single gasoline brand distributor. They can buy from whomever is cheapest on a given day. Dillons stores, which is under the Kroger umbrella, used to have an agreement with Texaco gasolines, but that was more due to location of the Texaco refinery than anything else. Now that Texaco in Kansas is nearly non-existent and the refinery belongs to someone else, I don't know how Dillons buys their gasolines.
All gasolines have to meet minimum govt specs for detergency, so there is probably no long term effects in using discount gas vs branded gas.
I use whatever is cheapest locally -- including Casey's, Sam's, Costco, Murphy USA, etc. Been doing about the same thing for about 10-15 years and have had no injector issues since 1991.
On trips where I am going to unfamiliar territory, I tend to stick with high traffic, Top Tier branded stations, because I have fewer options to complain if I find out I get a tank of bad gas.