Are kids allowed to catch their own limit of fish or do the fish count towards the licenced adults limit ?
It depends on if the children (under 14 years of age) are residents of the State of Idaho or nonresidents.
Resident children (primary domicile/home) who have lived in Idaho for at least the past 6 months are considered residents and can possess their own daily bag limit of fish. They can even purchase a salmon or steelhead permit (without having a license) and have their own bag limit of these fish. If they don't purchase a salmon or steelhead permit, then fish they catch and keep need to be recorded on their parents permit and count against their parent's daily bag limit.
Nonresident children (under the age of 14) can fish without a license, but they must be accompanied by a licensed individual (resident or nonresident). Any fish the youth catches count on the licensed person's daily bag limit. Nonresident youth can purchase their own 3-day Salmon and Steelhead permit and have their own limit of salmon or steelhead caught within the 3-day period covered by the license.