Probably best to ask the reserve staff on arrival. My experience was that they were very knowledgable and keen to help, so they should be able to steer if any are around.
The best places I reckon will be Island Mere (on the posts in the water - but quite distant) and probably from Bittern hide (although you're more looking down on the area, they would be closer). From what I recall kingfishers don't nest at Minsmere (no suitable sites), so Minsmere kingfishers appear later in the year, being fledged birds chased off a territory by mum & dad, who are trying for another brood. So this is actually the most likely time, probably through end September.
Wish you a great trip - always envious of a trip to Minsmere! I recommend The King's Head in Yoxford for good bar meals. There's also a really nice walk almost opposite King's Farm, on the road that runs north/south between Mill Road and Dunwich Road. It was recommended to us by one of the Minsmere staff, and was great for nightingale and turtle dove, we also saw woodlark early in the morning there.