Like I alluded to previously, trying to see S/KC and make it to Bakersfield in one day will be too rushed. I'd be happy with Visalia for the night, there are plenty of reasonably priced hotels there. Visalia to Flagstaff in one day is quite doable if you don't stop too much.
Yeah, I know it's only an hour farther to Bakersfield, but an extra hour the next day will be well worth it, giving you an extra hour in the park.