Birch Creek remains one of the best small streams for a youngster to try fly-fishing. At the family fishing area above Lone Pine the flow is stable, access is easy, fish are aggressive, and weather usually nice this time of year (only heavy wind and thunder showers compromise fishing success). Try wet flies early in the day and dry flies from late morning to early evening, and that youngster will have many chance at finding, hooking, playing, and releasing resident brookies and bows.
Looking for a bigger small stream? The Teton River in the basin might be one of the best currently if you remember to leave mid-day to recreational boaters and floaters. Try rusty spinners and terrestrial insect patterns in the early AM, and caddis life cycle and those terrestrial insect patterns during evening hours.