Strategy 1.
For children with earned income, self-employed parents should hire their children (which provides a deduction for the business at the parents’ rates and taxes the income at the kids’ rates);
Strategy 2.
For children with unearned income, pay careful attention to which brackets it will or won’t fall into, and consider whether it may be better to more aggressively try to shelter that income under the new kiddie tax rules (from buying municipal bonds, to zero-dividend stocks or tax-managed mutual funds, or leveraging a 529 plan).
Strategy 3.
Notably, though, because (for children age 18 or older) the kiddie tax rules only apply if the child is claimed as a dependent, parents may increasingly want to simply let young-adult children file for themselves (if the child can provide more than half of his/her own support), especially since the dependent exemption is gone anyway.
This article - understanding taxation of dependent children's income after tax reform is a good read.