KBG is a shallow rooting turf. The recommended rate is one inch of deep watering per application to promote deeper root growth and better drought resistance. Short, repetive watering will only promote this natural tendency and increase thatch. One inch of water per week should be sufficient to keep KBG from going dormant during a drought period. However, during the hot periods of summer, to keep that beautiful manicured look, 2 waterings a week may be needed.
Whether 45 min or 10 minutes is sufficient time to put down 1 inch of water is something you need to test. You can get spike style rain measuring gauges at some nursuries/stores or you can place empty cat or tuna cans around your lawn to run a test.
Clay is prone to run off or create standing water in low spots, so it may take one watering period followed by a second watering period 30 minutes later or longer to get 1 inch of water on the lawn without incuring run off or puddles in either period.
(Caveat: If you have reseeded the thin spots, you will only want to keep those areas damp and not allow them to dry out. Too much water on those areas can drown the seed or wash them away.)

Well, as usual I wasn't very thorough in my answer.

First, the amount of watering turf needs is dependent on the amount of rain that occurs, the type of soil (clays tend to have good water rentention), and temperature (affects water loss to evaporation). Observation of the turf (is it showing signs of water stress--dry blades, browning, etc.) will be the key to watering. In Spring and Fall, temperatures are usually lower and rainfall more aboundant so less watering will be needed.
Second, the same 1" per app per week rule(to keep it from dying during dry periods) should also be sufficient for your fescue (fescue is more deep rooting than KBG and can reach water that is deeper in the soil). Others will correct me if I'm wrong in regard to fescue.
Once again, deeper watering "trains" grass to deeper root, makes for a sturdier turf (won't tear up ealily) and makes it less suceptable to drought.

I am not aware of any study that has definitively reported how much water turf needs on a daily basis--probably because of the variables. If you can aford to water on a daily basis, I suppose it's moot. Hopefully someone will give you advice on any detriments to daily watering.