Kiddie tax does apply to unemployment income. But the child's unearned income is calculated after the $10,200 unemployment exclusion is applied. And the kiddie tax only applies to unearned income in excess of $2,200. So if your son's unemployment was $12,400 or less, and he had no other unearned income, there would be no kiddie tax.
The $10,200 unemployment exclusion is only for 2020.
