Should Zakat al-Fitr for children residing in America for schooling be given by their parents here, or by the children themselves there?

If there are poor people in the country where your sons will break their fast, then they should give their Zakat (definition) al-Fitr there for themselves. If they do not find needy people, or if there is someone in your country who is in greater need, then they may authorize you to give it on their behalf in your country. This will be sufficient for them if you give it with their knowledge. It will not be sufficient if you give it without their permission.