May a child who has reached the age of chinnuch eat meat during the nine days? Is there a difference if it is Friday evening dinner assuming the child eats before Shabbat begins?
Rav Shmuel Kamenetsky in קובץ הלכות - בין המצרים, פרק ט הלכה ב-ה writes:
1 - Up to around five years old - there are no restrictions.
2 - Erev Shabbos, if a child is eating his Shabbos meal before Shabbos, even meat is permitted. However, if he is eating again with the family at night, he should not have meat during the Friday daytime meal.
3 - Even during the week, bird meat [chicken] is permitted even for those children that are of chinuch age.
This article from Ohr Sameach Rabbi Yirmiyahu Ullman, says:
The custom is to refrain from eating meat and poultry or drinking wine and grape juice during the nine days. This also pertains to children.
(I assume that he is referring to children above the age of chinuch.)